^
19
ToFTrtE
tmiVEB$ITY
OF
University of California • Berkeley
1
CONVERSATIONS
THE ELEMENTS OF THAT SCIENCE
ARE
FAMILIARLY EXPLAINED,
AND ADAPTED TO THE
COMPREHENSION OF YOUNG PUPILS.
3(nu0trateii iDttti piate^.
BY THE AUTHOR OF CONVERSATIONS ON CHEMISTRV,
AND CONVERSATIONS ON POLITICAL
ECONOMY.
NEW-YORK :
PUBLISHED BY A. T. GOODRICH, W. B. GILLEY, AND CHARLES
WILEY k CO.
Clayton fy Kingdand, Printers.
1820.
^-^•-
A
5^^: V
recommendation/
The very pleasing style in which the Conver-
sations on Chemistry were written^ and the re-
markable clearness with which they illustrated
the leading facts 6/ that science^ have undqnbt-
edly contributed to render the study of it more
popular. The same observation applies to the
Conversations on Political Economy — a 'subr-
ject so obscure as to have been considered as
fit only for philosophers and statesmen has been
brought to the level of common understandings^
and devested of all its repulsive features. Upon
looking hastily into the present volume^ it ap-
pears to me to be distinguished by the same
clearness of elucidation as the former produc-
tions of the amiable author; and it will^ I have
no doubt^ prove to be a valuable addition to the
popular works on natural philosophy,
J. GRISCOM.
New-York, llth month 24th, 1819.
■is^y
*?«:>
PREFACE,
It is with increased diffidence that the
author offers this little work to the public.
The encouraging reception which the
Conversations on Chemistry and Political
Economy have met with, has induced her
to venture on publishing a short course on
Natural Philosophy ; but not without the
greatest apprehensions for its success.
Her ignorance of mathematics, and the
imperfect knowledge of natural philoso-
phy which that disadvantage necessarily
implies, renders her fully sensible of her
incompetency to treat the subject in any
other way than in the form of a familiar
explanation of the first elements, for the
use of very young pupils. It is the hope
of having done this in a manner that may
engage their attention, which encourages
her to offer them these additional lessons,
1*
VI PREFACE.
They are intended, in a course of ele-
mentary science, to precede the Conver-
sations on Chemistry; and were actually
written previous to either of her former
publications.
CONTENTS.
CONVERSATION I.
ON GENERAL PROPERTIES OF BODIES.
Introduction — General Properties of Bodies — Impenetrability >
Extension — Figure — Divisibility — Inertia — Attraction — At-
traction of Cohesion — Density — Rarity — Heat — Attraction of
Gravitation, 13
CONVERSATION II.
ON THE ATTRACTION OF GRAVITY.
Attraction of Gravitation, continued — Of Weight — Of the Fall
of Bodies — Of the Resistance of the Air — Of the Ascent of
Light Bodies, • 29
CONVERSATION III.
ON THE LAWS OF MOTION.
Of Motion — Of the Inertia of Bodies — Of Force to Produce
Motion — Direction of Motion — Velocity, absolute and rela-
tive— Uniform Motion — Retarded Motion — Accelerated iVIo-
tion — Velocity of Falling Bodies — Momentum — Action and
Reaction Equal — Elasticity of Bodies — Porosity of Bodies —
Reflected Motion — Angles of Incidence and Reflection, 43
CONVERSATION IV.
ON COMPOUND MOTION.
Compound Motion, the result of two opposite forces — Of Circu-
lar Motion, the result of two forces, one of which confines
the body to a fixed point — Centre of Motion, the point at rest
while the other parts of the body move round it — Centre of
Magnitude, the middle of a body — Centripetal Force, that
Vlll CONTENTS.
which confines a body to a fixed central point — Centrifugal
Force, that which impels a body to fly from the centre — Fall
of Bodies in a Parabola — Centre of Gravity, the Centre of
Weight, or point about which the parts balance each other, 59
CONVERSATION V.
ON THE MECHANICAL POWERS.
Of the Power of Machines — Of the Lever in General' — Of the
Lever of the first kind, having the Fulcrum between the
Power and the Weight — Of the Lever of the second kind,
having the Weight between the Power and the Fulcrum — Of
the Lever of the third kind, having the Power between the
Fulcrum and the Weight— Of the Pulley— Of the Wheel and
Axle— Of the Inclined Plane — Of the Wedge— of the Screw,
79
CONVERSATION VI.
ASTRONOMy.
CAUSES OF THE EARTH's ANNUAL MOTION.
Of the Planets, and their Motion — Of the Diurnal Motion of
the Earth and Planets, 90
CONVERSATION VII.
ON THE PLANETS.
Of the Satellites or Moons — Gravity Diminishes as the Square
of the Distance— Of the Solar System — Of Comets— Constel-
lations, signs of the Zodiac — Of Copernicus, Newton, kc. 102
CONVERSATION VIII.
ON THE EARTH.
Of the Terrestrial Globe— Of the Figure of the Earth— Of the
Pendulum— Of the Variation of the Seasons, and of the
Length of Days and Nights — Of the Causes of the Heat of
Summer— Of Solar, Sidereal, aad Equal or Mean Time, 114
CONTENTS. iX
CONVERSATION IX
ON THE MOON.
Of the Moon's Motion — Phases of the Moon — Eclipses of the
Moon — Eclipses of Jupiter's Moons — Of the Latitude and
Longitude — Of the Transits of the Inferior Planets — Of the
Tides, 134
CONVERSATION X.
HYDROSTATICS.
ON THE MECHANICAL PROPERTIES OF FLUIDS.
Definition of a Fluid — Distinction between Fluids and Liquids
— Of Non-Elastic Fluids, scarcely susceptible of Compression
— Of the Cohesion of Fluids — Of their Gravitation — Of their
Equilibrium—Of their Pressure — Of Specific Gravity — Of the
Specific Gravity of Bodies heavier than Water — Of those of
the same weight as Water — Of those lighter than Water — Of
the Specific Gravity of Fluids, 146
CONVERSATION XI.
OF SPRINGS, FOUNTAINS, k,C.
Of the Ascent of Vapour and the Formation of Clouds — Of the
Formation and Fall of Rain, &,c. — Of the Formation of
Springs — Of Rivers and Lakes — Of Fountains, 159
CONVERSATION XII.
PNEUMATICS.
ON THE MECHANICAL PROPERTIES OF AIR.
Of the Spring or Elasticity of the Air— Of the Weight of the Air
— Experiments with the Air Pump — Of the Barometer — Mode
of Weighing Air — Specific Gravity of Air — Of Pumps — De-
scription of the Sucking Pump— Description of the Forcing
Pump, 168
X CONTEWrS..
eONVERSATION XIII.
ON WIND AND SOUND.
Of Wind in General— Of the Trade Wind— Of the Periodica
Trade Winds— Of the Aerial Tides— Of Sound in General—
Of Sonorous Bodies— Of Musical Sounds— Of Concord or
Harmony, and Melody, ' 180
CONVERSATION XIV.
ON OPTICS.
Of Luminous, Transparent, and Opaque Bodies— Of the Radia-
tion of Light — Of Shadows — Of the Reflection of Light —
Opaque Bodies seen only by Reflected Light — Vision Ex-
plained— Camera Obscura — Image of Objects on the Retina,
194
CONVERSATION XV.
ON THE ANGLE OF VISION, AND THE REFLECTION OF MIRRORS.
Angle of Vision — Reflection of Plain Mirrors — Reflection of
Convex Mirrors — Reflection of Concave Mirrors, 208
CONVERSATION XVF.
ON REFRACTION AND COLOURS.
Transmission of Light by Transparent Bodies — Refraction —
Refraction of the Atmosphere — Refraction of a Lens — Re-
fraction of the Prism— Of the Colours of Rays of Light— Of
the Colours of Bodies, 223
CONVERSATION XVII.
OPTICS.
O^ THE STRUCTURE OF THE EYE, AND OPTICAL INSTRUMENTS.
Description of the Eye — Of the Image on the Retina — Refrac-
tion of the Humours of the Eye — Of the Use of Spectacles —
Of the Single Microscope — Of the Double Microscope — Of
the Solar Microscope — Magic Lauthorn — Refracting Tele-
scope— Reflecting Telescope, 241
DIRECTIONS
FOR PLACING THE ENGRAVINGS.
late I. to face page 34
II.
- 66
III.
62
IV.
- 70
V.
79
VI.
- - 91
VII.
- 104
VIII.
- 108
IX.
- 116
X.
- • - 128
XI.
- 132
XII.
- 136
XIII.
- 148
XIV.
- 164
XV.
- 195
XVI.
- 203
XVII.
- 208
XVIII.
. 217
XIX.
. 224
XX.
- 228
XXI.
- 241
XXII.
- .246
XXIII.
- 249
ERRATUM.
Page 62, for Plate III. read Plate IV.
CONVERSATION I.
ON GENERAL PROPERTIES OF BODIES.
Introduction. — General Properties of Bodies. — Impe-
netrability.— Extension. Figure. Divisibility. —
Inertia. — .Attraction. — Attraction of Cohesion. — Den-
sity.— Rarity. — Heat. — Attraction of Gravitation.
EjMILY. I must request your assistance, my dear
Mrs. B., in a charge which I have lately undertaken :
it is that of instructing my youngest sister, a task,
whicli I find proves more difficult than I had at first
imagined. I can teach her the common routine of
children's lessons tolerably well ; but she is such an
inquisitive little creature, that she is not satisfied
without an explanation of every difficulty that occurs
to her, and frequently asks me questions which I am
at a loss to answer. This morning, for instance,
when I had explained to her that the world was
round like a ball, instead of being flat as she had sup-
posed, and that it was surrounded by the air, she ask-
ed me what supported it. I told her that it required
no support ; she then inquired why it did not fall as
every thing else did ? This I confess perplexed me ;
for I had myself been satisfied with learning that the
world floated in the air, without considering how un-
natural it was that so heavy a body, bearing the weight
of all other things, should be able to support itself.
Mrs. B. 1 make no doubt, my dear, but that 1 shall
be able to explain this difficulty to you ; but I believe
that it would be almost impossible to render it intelli-
2
14 GENERAL PROrERTiES OF BODIES.
gible to the comprehension of so young a child as
your sister Sophia. You, who are now in your thir-
teenth year, may, I think with great propriety, learn
not only the cause of this particular fact, but acquire
a general knowledge of the laws by which the natural
world is governed.
Emily. Of all things, it is what I should most like
to learn ; but I was afraid it was too difficult a study
even at my age.
Mrs. B. Not when familiarly explained : if you
have patience to attend, I will most willingly give you
all the information in my power. You may perhaps
find the subject rather dry at first ; but if I succeed
in explaining the laws of nature, so as to make you
understand them, I am sure that you will derive not
only instruction, but great amusement from that
study.
Emily. I make no doubt of it, Mrs. B. ; and pray
begin by explaining why the earth requires no sup-
port ; for that is the point which just now most strong-
ly excites my curiosity.
Mrs. B. My dear Emily, if I am to attempt to give
you a general idea of the laws of nature, which is no
less than to introduce you to a knowledge of the sci-
ence of natural philosophy, it will be necessary for us
to proceed with some degree of regularity. I do not
wish to confine you to the systematic order of a scien-
tific treatise ; but if we were merely to examine eve-
ry vague question that may chance to occur, our pro-
gress would be but very slow. Let us, therefore^
begin by taking a short survey of the general proper-
ties of bodies, some of which must necessarily be ex-
plained before I can attempt to make you understand
Tvhy the earth requires no support.
When I speak of bodies, I mean substances, of what-
ever nature, whether solid or fluid ; and matter is the
general term used to denote the substance, whatever
its nature be, of which the different bodies are com-
posed. Thus, wood is tliQ matter of which this table
GENERAL PROPERTIES OF BODIES. lb
IS made ; water is the matter with which this glass is
tilled, &c-
Emily. I am very glad you have explained the
meaning of the word matter, as it has corrected an er-
roneous conception I had formed of it : I thought that
it was applicable to solid bodies only.
Mrs. B. There are certain properties which ap-
pear to be common to all bodies, and are hence called
the essential properties of bodies ; these are, Impene-
(rability, Extension, Figure, Divisibility, Inertia, and
Attraction. These arc called the general properties
of bodies, as we do not suppose any body to exist with-
out them.
By impenetrability, is meant the property which
bodies have of occupying a certain space, so that,
where one body is, another cannot be, without dis-
placing the former ; for tvvo bodies cannot exist in the
same place at the same time. A liquid may be more
easily removed than a solid body ; yet it is not the
less substantial, since it is as impossible for a liquid
and a solid to occupy the same space at the same time,
as for two solid bodies to do so. For instance, if you
put a spoon into a glass full of water, the water will
flow over to make room for the spoon.
Emily. 1 understand this perfectly. Liquids are
in reality as substantial or as impenetrable as solid
bodies, and they appear less so, only because they
are more easily displaced.
Mrs. B. The air is a fluid differing in its nature
from liquids, but no less impenetrable. If I endea-
vour to till this phial by plunging it into this basin of
water, the air, you see, rushes out of the phial in
bubbles, in order to make way for the water, for the
air and the water cannot exist together in the same
space, any more than two hard bodies ; and if I re-
verse this goblet, and plunge it perpendicularly into
the water, so that the air will not be able to escape,
the water will no longer be able to till the goblet.
Emily, But it rises a considerable way into the
glass.
16 GENERAL PROPERTIES OF BODIES.
Mrs. B. Because the water compresses or
squeezes the air into a small space in the upper part
of the glass . but, as long as it remains there, no
other body can occupy the same place.
Emily. A difficulty has just occurred to me, with
regard to the impenetrability of solid bodies ; if a
nail is c!riven into a piece of wood, it penetrates it,
and both the wood and the nail occupy the same space
that the wood alone did before ?
Mrs. B. The nail penetrates between the parti-
cles of the V ood, by forcing them to make way for
it; for you know that not a single atom of wood can
remain in the space which the nail occupies ; and if
the wooo is not increased in size by the addition of the
nail, it is because wood is a porous substance, like
sponge, the particles of which may be compressed or
squeezed closer together ; and it is thus that they
make way for the nail.
We may now proceed to the next general property
(ji bodies, extension. A body which occupies a cer-
tain space must necessarily have extension ; that is to
say, length, breadth, and depth; these are called the
dimensions of extension : can you form an idea of any
body without them ?
Emily. No ; certainly I cannot ; though these di-
mensions must, of course, vary extremely in different
bodies. The length, breadth, and depth of a box, or
of a tJ. nble, are very different from those of a walk-
ing-stic'., or of a hair.
But is not height also a dimension of extension ?
Mrs. B. Height and depth are the same dimension,
considered in different points of view ; if you measure
a body, or a space, from the top to the bottom, you
call it depth ; if from the bottom upwards, you call it
height ; thus the depth and height of a box are, in
fact, the same thing.
Emily. Very true ; a moment's consideration
%vould have enabled me to discover that ; and breadth
and width are also the same dimension.
Mrs. B. Yes ; the limits of extension constitute
GENERAL PROPERTIES OP BODIES. 17
figure or shape. You conceive that a body having
length, breadth, and depth, cannot be without form,
either symmetrical or irregular ?
Emily. Undoubtedly ; and this property admits of
almost an infinite variety.
Mrs. B. Nature has assigned regular forms to her
productions in general. The natural form of mineral
substances is that of crystals, of which there is a great
variety. Many of them are very beautiful, and no
less remarkable by their transparency, or colour, than
by the perfect regularity of their forms, as may be
seen in the various museums and collections of natu-
ral history. The vegetable and animal creation ap-
pears less symmetrical, but is still more diversified in
figure than the mineral kingdom. Manufactured sub-
stances assume the various arbitrary forms which the
art of man designs for them; and an infinite number
of irregular forms are produced by fractures, and by
the dismemberment of the parts of bodies.
Emily. Such as a piece of broken china, or glass ?
Mrs. B. Or the fragments of mineral bodies which
are broken in being dug out of the earth, or decayed
by the effect of torrents and other causes. The pic-
turesque effect of rock-scenery is in a great measure
owing to accidental irregularities of this kind.
We may now proceed to divisibility ; that is to say,
a susceptibility of being divided into an indefinite num-
ber of parts. Take any small quantity of matter, a
grain of sand for instance, and cut it into two parts;
these two parts might be again divided, had we in-
struments sufficiently fine for the purpose ; and if, by-
means of pounding, grinding, and other similar me-
thods, we carry this division to the greatest possible
extent, and reduce the body to its finest imaginable
particles, yet not one of the particles will be destroy-
ed, and the body will continue to exist, though in this
altered state.
The melting of a solid body in a liquid affords a ve-
ry striking example of the extreme divisibility of mat-
ter ; when you sweeten a cup of tea, for instance,
2*
18 GENERAL PROPERTIES OT BODTES.
with what minuteness the sugar must be divided to be
diffused throughout the whole of the hquid.
Emily. And if you pour a few drops of red wine
into a glass of water, they immediately tinge the
whole of the water, and must therefore be diffused
throughout it.
Mrs. B. Exactly so ; and the perfume of this la-
vender-water will be almost as instantaneously diffu-
sed throughout the room, if I take out the stopper.
Emily., But in this case it is only the perfume of
the lavender, and not the water itself, that is diffused
in the room ?
Mrs. B. The odour or smell of a body is part of
the body itself, and is produced b}' very minute parti-
cles or exhalations which escape from odoriferous bo-
dies. It would be impossible that you should smell
the lavender-water, if particles of it did not come in
actual contact with your nose.
Emily. But when I smell a flower, I see no va-
pour rise from it ; and yet I can perceive the smell
at a considerable distance.
Mrs. B. You could, I assure you, no more smell
a flower, the odoriferous particles of which did not
touch your nose, than you could taste a fruit, the
flavoured particles of which did not come in contact
with your tongue.
Emily. That is wonderful indeed; the particles
then, which exhale from the flower and from the la-
vender-water, are, I suppose, too small to be visible ?
Mrs. B. Certainly : you may form some idea of
their extreme minuteness, from the immense number
which must have escaped in order to perfume the
whole room ; and yet there is no sensible diminution
of the liquid in the phial.
Emily. But the quantity must really be diminish-
ed?
Mrs. B. Undoubtedly ; and were you to leave
the bottle open a sufficient length of time, the whole
of the water would evaporate and disappear. But
though so minutely subdivided as to be imperceptible
GENERAL PROPERTIES OF BODIES. 19-
to any of our senses, each particle would continue to
exist ; for it is not within the power of man to de-
stroy a single particle of matter ; nor is there any rea-
son to suppose that in nature an atom is ever annihi-
lated.
Emily. Yet, when a body is burnt to ashes, part
of it, at least, appears to be effectually destroyed ?
Look how small is the residue of ashes beneath the
grate, from all the coals which have been consumed
within it.
Airs. B. That part of the coals, which you sup-
pose to be destroyed, evaporates in the form of
smoke and vapour, whilst the remainder is reduced
to ashes. A body, in burning, undergoes no doubt
very remarkable changes ; it is generally subdivided ;
its form and colour altered ; its extension increased :
but the various parts, into which it has been separa-
ted by combustion, continue in existence, and retain
all the essential properties of bodies.
Emily. But that part of a burnt body which eva-
porates in smoke has no figure : smoke, it is true, as-
cends in columns into the air, but it is soon so much
diffused as to lose all form; it becomes indeed invisi-
ble.
Mrs. B. Invisible, I allow ; but we must not ima-
gine that what we no longer see no longer exists.
Were every particle of matter that becomes invisible
annihilated, the world itself would in the course of
time be destroyed. The particles of smoke, when
difi'used in the air, continue still to be particles of
matter, as well as when more closely united in the
form of coals: they are really as substantial in the
one state as in the other, and equally so when by
their extreme subdivision they become invisible. No
particle of matter is ever destroyed : this is a princi-
ple you must constantly remember. Every thing in
nature decays and corrupts in the lapse of time. We
die, and our bodies moulder to dust ; but not a single
atom of them is lost ; they serve to nourish the earth,
whence, while living, they drew their support.
20 GfiT!?ERAL PROPERTIES OF BODIES.
The next essential property of matter is called in-
ertia; this word expresses the resistance which inac-
tive matter makes to a change of state. Bodies ap-
pear to be equally incapable of changing their actual
state, whether it be of motion or of rest. You know
that it requires force to put a body which is at rest ia
motion ; an exertion of strength is also requisite to
stop a body which is already in motion. The resist-
ance of the body to a change of state, in either case,
is called its inertia.
Emily. In playing at base-ball I am obliged to use
all my strength to give a rapid motion to the ball ; and
when I have to catch it, I am sure I feel the'resistance
it makes to being stopped. But if I did not catch it,
it would soon fall to the ground and stop of itself.
Mrs. B. Inert matter is as incapable of stopping of
itself, as it is of putting itself into motion: when the
ball ceases to move, therefore, it must be stopped by
some other cause or power; but as it is one with
which you are yet unacquainted, we cannot at present
investigate its effects.
The last property which appears to be common to
all bodies is attraction. All bodies consist of infinite-
ly small particles of matter, each of which possesses
the power of attracting or drawing towards it, and
uniting with any other particle sufficiently near to be
within the influence of its attraction ; but in minute
particles this power extends to so very small a dis-
tance around them, that its effect is not sensible, un-
less they are (or at least appear to be) in contact; it
then makes them stick or adhere together, and is
hence called the attraction of cohesion. Without this
power, solid bodies would fall in pieces, or rather
crumble to atoms.
Emily. I ara so much accustomed to see bodies
firm and solid that it never occurred to me that any
power was requisite to unite the particles of which
they are composed. But the attraction of cohesion
does not, 1 suppose, exist in liquids ; for the particles
GENERAL PROPERTIES OF BODIES. 21
of liquids do not remain together so as to form a body,
unless confined in a vessel ?
Mrs. B. I beg your pardon ; it is the attraction of
cohesion which holds this drop of water suspended
at the end of ray finger, and keeps the minute watery
particles of which it is composed united. But as
this power is stronger in proportion as the particles
of bodies are more closely united, the cohesive at-
traction of solid bodies is much greater than that of
fluids.
The thinner and lighter a fluid is, the less is the co-
hesive attraction of its particles,because they are fur-
ther apart; and in elastic fluids, such as air, there is
no cohesive attraction among the particles.
Emily. That is very fortunate ; for it would be im-
possible to breathe the air in a solid mass ; or even in
a liquid state.
But is the air a body of the same nature as other
bodies ?
Mrs. B. Undoubtedly, in all essential properties.
Emily. Yet you say that it does not possess one
of the general properties of bodies — cohesive attrac-
tion?
Mrs. B. The particles of air are not destitute of
the power of attraction, but they are too far distant
from each other to be influenced by it; and the ut-
most efforts of human art have proved ineff*ectual in
the attempt to compress them, so as to bring them
within the sphere of each other's attraction, and make
them cohere.
Emily. If so, how is it possible to prove that they
are endowed with this power?
Mrs. B. The air is formed of particles precisely
of the same nature as those which enter into the com-
position of liquid and solid bodies, in which state we
have a proof of their attraction.
Emily. It is then, I suppose, owing to the diff*er-
ent degrees of attraction of diff'erent substances, that
they are hard or soft; and that liquids are thick or
thin ?
22 GENERAL PROPERTIES OF BODIES,
Mrs. B. Yes ; but you would express your meati-
ing better by the term density, which denotes the de-
gree of closeness and compactness of the particles of
a body : thus you may say, both of solids and of li-
quids, that the stronger the cohesive attraction, the
greater is the density of the body. In philosophical
language, density is said to be that property of bodies
by which they contain a certain quantity of matter,
under a certain bulk or magnitude. Rarity is the
cor»trary of density ; it denotes the thinness and sub-
tlety of bodies : thus you would say that mercury or
quicksilver was a very dense fluid ; ether, a very
rare one, &c.
Caroline. But how are we to judge of the quantity
of matter contained in a certain bulk?
Mrs. B. By the weight: under the same bulk,
bodies are said to be dense in proportion as they are
heavy.
Emily. Then we may say that metals are dense
bodies, wood comparatively a rare one, &c. But,
Mrs. B., when the particles of a body are so near as
to attract each other, the effect of this power must
increase as they are brought by it closer together ;
so that one would suppose that the body would gra-
dually augment in density, till it was impossible for
its particles to be more closely united. Now, we
know that this is not the case ; for soft bodies, such
as cork, sponge, or butter, never become, in conse-
quence of the increasing attraction of their particles,
as hard as iron ?
Mrs. B. In such bodies as cork and sponge, the
particles which come in contact are so few as to pro-
duce but a slight degree of cohesion : they are po-
rous bodies, which, owing to the peculiar arrange-
ment of their particles, abound with interstices which
separate the particles ; and these vacancies are filled
with air, the spring or elasticity of which prevents
the closer union of the parts. But there is another
fluid much more subtle than air, which pervades all
bodies, this is heat. Heat insinuates itself more or
GENERAL PROPERTIES OF BODIES. 23
less between the particles of all bodies, and forces
them asunder ; you may therefore consider heat, and
the attraction of cohesion, as constantly acting in op-
position to each other.
Emily. The one endeavouring to rend a body to
pieces, the other to keep its parts firmly united.
Mrs. B. And it is this struggle between the con-
tending forces of heat and attraction, which prevents
the extreme degree of density which would result
from the sole influence of the attraction of cohesion.
Emily. The more a body is heated then, the more
its particles will be separated.
Mrs. B, Certainly : we find that bodies swell or
dilate by heat : this effect is very sensible in butter,
for instance, which expands by the application of heat,
till at length the attraction of cohesion is so far dimi-
nished that the particles separate, and the butter be-
comes liquid. A similar effect is produced by heat
on metals, and all bodies susceptible of being melted.
Liquids, you know, are made to boil by the appli-
cation of heat ; the attraction of cohesion then yields
entirely to the expansive po>ver ; the particles are
totally separated and converted into steam or va-
pour. But the agency of heat is in no body more
sensible than in air, which dilates and contracts by
its increase or diminution in a very remarkable de-
gree.
Emily. The effects of heat appear to be one of
the most interesting parts of natural philosophy.
Mrs. B. That is true ; but heat is so intimately
connected with chemistry, that you must allow me to
defer the investigation of its properties till you be-
come acquainted with that science. To return to its
antagonist, the attraction of cohesion ; it is this pow-
er which restores to vapour its liquid form, which
unites it into drops when it falls to the earth in a show-
er of rain, which gathers the dew into brilliant gems
on the blades of grass.
Emily. And I have often observed that after a
shower, the water collects into large drops on the
'24 GENERAL PROPERTIES OF BODIES.
leaves of plants ; but I cannot say that I perfectly unr
derstand how the attraction of cohesion produces this
effect.
Mrs. B. Rain does not fall from the clouds in the
form of drops, but in that of mist or vapour, which is
composed of very small watery particles ; these, in
their descent, mutually attract each other, and those
that are sufficiently near in consequence unite and
form a drop, and thus the mist is transformed into a
shower. The dew also was originally in a state of
vapour, but is, by the mutual attraction of the parti-
cles, formed into small globules on the blades of grass :
in a similar manner the rain upon the leaf collects in-
to large drops, which, when they become too heavy
for the leaf to support, fall to the ground.
Emily. All this is wonderfully curious ! I am al-
most bewildered with surprise and admiration at the
number of new ideas I have already acquired.
Mrs. B. Every step that you advance in the pur-
suit of natural science, will fill your mind with admi-
ration and gratitude towards its Divine Author. In
the study of natural philosophy, we must consider
ourselves as reading the book of nature, in which the
bountiful goodness and wisdom of God is revealed to
all mankind ; no study can then tend more to purify
the heart, and raise it to a religious contemplation of
the Divine perfections.
There is another curious effect of the attraction of
cohesion which I must point out to you. - It enables
liquids to rise above their level in capillary tubes :
these are tubes the bores of which are so extremely
small that liquids ascend within them, from the cohe-
sive attraction between the particles of the liquid and
the interior surface of the tube. Do you perceive
the water rising above its level in this small glass
tube, which I have immersed in a goblet full of water ?
Emily. Oh yes ; I see it slowly creeping up the
tube, but now it is stationary : will it rise no higher ?
Mrs. B. No ; because the cohesive attraction be-
tween the water and the internal surface of the tube
GENERAL PROPERTIES OF BODIES. 26
is now balanced by the weight of the water within it :
if the bore of the tube were narrower the water
would rise higher; and if you immerse several tubes
of bores of different sizes, you will see it rise to differ-
ent heights in each of them. In making this expe-
riment you should colour the water with a little red
wine, in order to render the effect more obvious.
All porous substances, such as sponge, bread, linen,
&c., may be considered as collections of capillary
tubes : if you dip one end of a lump of sugar into wa-
ter, the water will rise in it, and wet it considerably
above the surface of that into which you dip it.
Emily. In making tea I have often observed that
effect, without being able to account for it,
Mrs. B. Now that you are acquaintted with the
attraction of cohesion, I must endeavour to explain to
you that oi Gravitation, which is a modification of the
same power ; the first is perceptible only in very mi-
nute particles, and at very small distances ; the other
acts on the largest bodies, and extends to immense
distances.
Emily. You astonish me : surely you do not mean
to say, that large bodies attract each other.
Mrs. B. Indeed I do : let us take, for example,
one of the largest bodies in nature, and observe whe-
ther it does not attract other bodies. What is it that
occasions the fall of this book, when I no longer sup-
port it?
Emily. Can it be the attraction of the earth ? I
thought that all bodies had a natural tendency to fall.
Mrs. B. They have a natural tendency to fall, it
is true ; but that tendency is produced entirely by
the attraction of the earth : the earth being so much
larger than any body on its surface, forces every body,
which is not supported, to fall upon it
Emily. If the tendency which bodies U,ave to fall
results from the earth's attractive power, the earth
itself can have no such tendency, since it cannot at-
tract itself, and therefore it requires no support to
prevent it from falling. Yet the idea that bodies do
3
Jb GENERAL PROPERTIES OJP BODIES.
not fall of their own accord, but that they are drawn
towards the earth by its attraction, is so new and
strange to me, that I know not how to reconcile my-
self to it.
Mrs. B. When you are accustomed to consider the
fall of bodies as depending on this cause, it will ap-
pear to you as natural, and surely much more satisfac-
tory, than if the cause of their tendency to fall were
totally unknown. Thus you understand, that all
matter is attractive, from the smallest particle to the
largest mass ; and that bodies attract each other with
a force proportional to the quantity of matter they
contain.
Emily. I do not perceive any difference between
the attraction of cohesion and that of gravitation ; is
it not because every particle of matter is endowed
with an attractive power, that large bodies, consist-
ing of a great number of particles, are so strongly at-
tractive ?
Mrs. B. True. There is, however, this differ-
ence between the attraction of particles and that of
masses, that the former is stronger than the latter, in
proportion to the quantity of matter. Of this you
have an instance in the attraction of capillary tubes,
in which liquids ascend by the attraction of cohesion,
in opposition to that of gravity. It is on this account
that it is necessary that the bore of the tube should be
extremely small; for if the column of water within
the tube is not very minute, the attraction would not
be able either to raise or support its weight, in oppo-
sition to that of gravity.
You may observe, also, that all solid bodies are
enabled by the force of the cohesive attraction of
their particles to resist that of gravity, which would
otherwise disunite them, and bring them to a level
with the ground, as it does in the case of liquids, the
cohesive attraction of which is not sufficient to enable
it to resist the power of gravity.
Emily. And some solid bodies appear to be of this
GENERAL PROPERTIES OF BODIES. 27
nature, as sand and powder for instance ; there is no
attraction ofcohesion between their particles ?
Mrs. B. Every grain of powder or sand is com-
posed of a great number of other more minute parti-
cles, tirmly united by the attraction ofcohesion ; but
amongst the separate grains there is no sensible at-
traction, because they are not in sufficiently close
contact.
Emily. Yet they actually touch each other ?
Mrs. B. The surf<ice of bodies is in general so
rough and uneven, that when in actual contact, they
touch each other only by a ^qw points. Thus, if I
lay upon the table this book, the binding of which ap-
pears perfectly smooth, yet so few of the particles of
its under surface come in contact with the table, that
no sensible degree of cohesive attraction takes place ;
for you see, that it does not stick, or cohere to the
table, and I find no difficulty in lifting it off.
It is only when surfaces perfectly flat and well po-
lished are placed in contact, that the particles ap-
proach in sufficient number, and closely enough to
produce a sensible degree of cohesive attraction*
Here are two hemispheres of polished metal, I press
their flat surfaces together, having previously inter-
posed a {qw drops of oil, to fill up every little porous
vacancy. Now try to separate them.
Emily. It requires an eflbrt beyond my strength,
though there are handles for the purpose of pulling
them asunder. Is the firm adhesion of the two
hemispheres merely owing to the attraction of cohe-
sion
Mrs. B. There is no force more powerful, since
it is by this that the particles of the hardest bodies
are held together. It would require a weight of se-
veral pounds to separate these hemispheres.
Emily. In making a kaleidoscope, I recollect that
the two plates of glass, which were to serve as mir-
rors, stuck so fast together, that I imagined some of
the gum I had been using had by chance been inter-
posed between them ; but now I make no doubt but
28 GENERAL PROPERTIES OF BODIES.
that it was their own natural cohesive attractioii
which produced this effect.
Mrs. B. Very probably it was so ; for plate-glass
has an extremely smooth flat surface, admitting of the
contact of a great number of particles, between two
plates, laid one over the other.
Emily. But, Mrs. B., the cohesive attraction of
some bodies is much greater than that of others ;
thus glue, gum, and paste, cohere with singular tena-
city.
Mrs. B. That is owing to the peculiar chemical
properties of those bodies, independently of their co-
hesive attraction.
There are some other kinds or modifications of at-
traction peculiar to certain bodies ; namely, that of
magnetism, and of electricity ; but we shall confine
our attention merely to the attraction of cohesion and
of gravity ; the examination of the latter we shall re-
sume at our next meeting.
CONVERSATION 11.
ON THE ATTRACTION OF GRAVITY.
Attraction of Gravitation, continued. — Of Weight. —
Of the Fall of Bodies. — Of the Resistance of the Air.
— Of the Ascent of Light Bodies.
EjMILY. I have related to my sister Caroline all
that you have taught me of natural philosophy, and
she has been so much delighted by it, that she hopes
you will have the goodness to admit her to your les-
sons.
Mrs. B. Very willingly ; but I did not think you
had any taste for studies of this nature, Caroline?
Caroline. I confess, Mrs. B., that hitherto I had
formed no very agreeable idea, either of philosophy,
or philosophers ; but what Emily has told me, has
excited my curiosity so much, that I shall be highly
pleased if you will allow me to become one of your
pupils.
Mrs. B. I fear that I shall not find you so tract-
ablie a scholar as Emily ; I know that you are much
biassed in favour of your own opinions.
Caroline. Then you will have the greater meri{ in
reforming them, Mrs. B. ; and after all the wonders
that Emily has related to me, I think I stand but little
chance against you and your attractions.
Mrs. B. You will, 1 doubt not, advance a number
of objections ; but these I shall willingly admit, as
they will be a means of elucidating the subject.
Emily, do you recollect the names of the general pro-
perties of bodies?
3*
30 ON THE ATTRACTION OF GRAVITY.
Emily. Impenetrability, extension, figure, divisi-
bility, inertia, and attraction.
Mrs, B. Very well. You must remember that
these are properties common to all bodies, and of
which they cannot be deprived ; all other properties of
bodies are called accidental, because they depend on
the relation or connexion of one body to another.
Caroline. Yet surely, Mrs. B., there are other
properties which are essential to bodies, besides those
you have enumerated. Colour and weight, for in-
stance, are common to all bodies, and do not arise
from their connexion with each other, but exist in
the bodies themselves ; these, therefore, cannot be
accidental qualities ?
Mrs. B. I beg your pardon ; these properties do
not exist in bodies independently of their connexion
with other bodies.
Caroline. What I have bodies no weight? Does
not this table weigh heavier than this book; and, if
one thing weighs heavier than another, must there
not be such a thing as weight?
Mrs. B. No doubt : but this property does not ap-
pear to be essential to bodies ; it depends upon their
connexion with each other. Weight is an effect of
the power of attraction, without which the table and
the book would have no weight whatever.
Emily. I think 1 understand you ; is it not the at-
traction of gravity, which makes bodies heavy ?
Mrs. B. You are right. I told you that the at-
traction of gravity was proportioned to the quantity of
matter which bodies contained ; now the earth con-
sisting of a much greater quantity of matter than any
body upon its surface, the force of its attraction must
necessarily be greatest, and must draw every thing
towards it; in consequence of which, bodies that are
unsupported fall to the ground, whilst those that are
supported press upon the object which prevents
their fall, with a weight equal to the force with
which they gravitate towards the earth.
Caroline. The same cause then which occasion?
ON THE ATTRACTION OP GRAVITr. 31
the fall of bodies, produces also their weight. It was
very dull in me not to understand this before, as it is
the natural and necessary consequence of attraction ;
but the idea that bodies were not really heavy of
themselves, appeared to me quite incomprehensible.
But, Mrs. B., if attraction is a property essential to
matter, weight must be so likewise ; for how can one
exist without the other ?
Mrs. B. Suppose there were but one body exist-
ing in universal space, what would its weight be ?
Caroline. That would depend upon its size ; or,
more accurately speaking, upon the quantity of mat-
ter it contained.
Emily. No, no ; the body would have no weight,
whatever were its size ; because nothing would at-
tract it. Am 1 not right, Mrs. B. ?
Mrs. B. You are ; you must allow, therefore,
that it would be possible for attraction to exist with-
out weigi.t ; for each of the particles of which the
body was composed, would possess the power of at-
traction ; but they could exert it only amongst them-
selves ; the whole mass, having nothing to attract, or
to be attracted by, would have no weight.
Caroline. 1 am now well satisfied that weight is
not essential to the existence of bodies ; but what
have you to object to colours, Mrs. B. ; you will not,
I think, deny that they really exist in the bodies
themselves.
Mrs. B. When we come to treat of the subject of
colours, I trust that I shall be able to convince you,
that colours are likewise accidental qualities, quite
distinct from the bodies to which they appear to belong.
Caroline. Ob do pray explain it to us now, I am
so very curious to know how that is possible.
Mrs. B. Unless we proceed with some degree of
order and method, you will in the end find yourself
but little the wiser for all you learn. Let us there-
fore go on regularly, and make ourselves well ac-
quainted with the general properties of bodies, before
we proceed further.
32 ON THE ATTRACTION OF GRAVITY.
Emily. To return, then, to attraction, (which ap-
pears to me by far the most interesting of them, since
it belongs equally to all kinds of matter,) it must be
mutual between two bodies; and if so, when a stone
falls to the earth, the earth should rise part of the way
to meet the stone ?
Mrs. B. Certainly ; but you must recollect that
the force of attraction is proportioned to the quantity
of matter which bodies contain, and if you consider
the difference there is in that respect, between a
stone and the earth, you will not be surprised that
you do not perceive the earth rise to meet the stone ;
for though it is true that a mutual attraction takes
place between the earth and the stone, that of the
latter is so very small in comparison to that of the
former, as to render its effect insensible.
Emily. But since attraction is proportioned to
the quantity of matter which bodies contain, why do
not the hills attract the houses and churches towards
them ?
Caroline. Heavens, Emily, what an idea 1 How
can the houses and churches be moved, when they
are so firmly fixed in the ground ?
Mrs. B. Emily's question is not absurd, and your
answer, Caroline, is perfectly just ; but can you tell
lis why the houses and churhes are so firmly fixed in
the ground ?
Caroline. I am afraid I have answered right by
mere chance ; for 1 begin to suspect that bricklayers
and carpenters could give but little stability to theit
buildings, without the aid of attraction.
Mrs. B. It is certainly the cohesive attraction
between the bricks and the mortar, which enables
them to build walls, and these are so strongly attract-
ed by the earth, as to resist every other impulse ;
otherwise they would necessarily move towards the
hills and the mountains ; but the lesser force must
yield to the greater. There are, however, some
circumstances in which the attraction of a large body
has sensibly counteracted that of the earth. If,
ON THE ATTRACTION OF GRAVITY. 33
whilst standing on the declivity of a mountain, you
hold a plumb-line in your hand, the weight will not
fall perpendicular to the earth, but incline a little to-
wards the mountain ; and this^ owing to the lateral,
or sideways attraction of the mountain, interfering
with the perpendicular attraction of the earth.
Emily. But the size of a mountain is very trifling,
compared to the whole earth ?
Mrs. B. Attraction, you must recollect, diminishes
with distance ; and in the example of the plumb-line,
the weight suspended is considerably nearer to the
mountain than to the centre of the earth.
Caroline. Pray, Mrs. B., do the two scales of a
balance hang parallel to each other ?
Mrs. B. You mean, I suppose, in other words, to
inquire whether two lines which are perpendicular to
the earth, are parellel to each other ? I believe I
guess the reason of your question? but I wish you
would endeavour to answer it without my assistance.
Caroline. I was thinking that such lines must both
tend by gravity to the same point, the centre of the
earth ; now lines tending to the same point cannot be
parallel, as parallel lines are always at an equal dis-
tance from each other, and would never meet.
Mrs. B. Very well explained : you see now the
use of your knowledge of parallel lines ; had you
been ignorant of their properties, you could not have
drawn such a conclusion. This may enable you to
form an idea of the great advantage to be derived
even from a slight knowledge of geometry, in the stu-
dy of natural philosophy ; and if, after I have made
you acquainted with the first elements, you should be
tempted to pursue the study, I would advise you to
prepare yourselves by acquiring some knowledge of
geometry. This science would teach you that lines
which fall perpendicular to the surface of a sphere
cannot be parallel, because they would all meet, if
prolonged to the centre of the sphere ; while lines
that fall perpendicular to a plane or flat surface, are
34 ON THE ATTRACTION OF GRAVITY.
always parallel, because, if prolonged, they would
never meet.
Emily. And yet a pair of scales, hanging perpen-
dicular to the earth, aopear parallel?
Mrs. B. Because the sphere is so large, and the
scales consequently converge so little, that their in-
clination is not perceptible to our senses ; if we
could construct a pair of scales whose beam would
extend several degrees, their convergence would be
very obvious ; but as this cannot be accomplished,
let us draw a small tigure of the earth, and then we
may make a pair of scales of the proportion wc
please, (fig. 1. Plate I.)
Caroline. This figure renders it very clear : then
two bodies cannot fall to the earth in parallel lines ?
Mrs. B. Never.
Caroline. The reason that a heavy body falls
quicker than a light one, is, I suppose, because the
earth attracts it more strongly ?
Mrs. B. The earth, it is true, attracts a heavy
body more than a light one ; but that would not
make the one fall quicker than the other.
Caroline. Yet, since it is attraction that occasions
the fall of bodies, surely the more a body is attracted,
the more rapidly it will fall. Besides, experience
proves it to be so. Do we not every day see heavy
bodies fall quickly, and light bodies slowly.
Emily. It strikes me, as it does Caroline, that as
attraction is proportioned to the quantity of matter,
the earth must necessarily attract a body which con-
' tains a great quantity more strongly, and therefore
bring it to the ground sooner than one consisting of
a smaller quantity.
Mrs. B. You must consider, that if heavy bodies
are attracted more strongly than light ones, they re-
quire more attraction to make them fall. Remem-
ber that bodies have no natural tendency to fall, any
more than to rise, or to move laterally, and that they
will not fall unless impelled by some force ; now
this force must be proportioned to the quantity of
TLATE I.
Jij. 2.
%• 1-
ON THE ATTRACTION OF GRAVITY. 35
matter it has to move : a body consisting of 1000
particles of matter, for instance, requires ten times as
much attraction to bring it to the ground in the
same space of time as a body consisting of only 100
particles.
Caroline. I do not understand that ; for it seems
to me, that the heavier a body is, the more easily and
readily it falls.
Emily. I think I now comprehend it : let me try
if I can explain it to Caroline. Suppose that 1 draw
towards me two weighty bodies, the one of lOOlbs.
the other of lOOOlbs., must I not exert ten times as
much strength to draw the larger one to me, in the
same space of time as is required for the smaller one ?
Aij if the earth draws a body of lOOOlbs. weight to it
in the same space of time that it draws a body of
lOOlbs., does it not follow that it attracts the body of
lOOOlbs. weight with ten times the force that it does
that of lOOlbs.?
Caroline. 1 comprehend your reasoning perfectly ;
but if it were so, the body of lOOOlbs. weight, and
that of lOOlbs. would fall with the same rapidity;
and the consequence would be, that all bodies, whe-
ther light or heavy, being at an equal distance from
the ground, would fall to it in the same space of time :
now it is very evident that this conclusion is absurd ;
experience eve- stant contradicts it: observe how
much sooner this book reaches the floor than this
sheet of paper, when 1 let them drop together.
Emily. That is an objection I cannot answer. I
must refer it to you, Mrs. B.
Mrs. B. I trust that we shall not find it insurmount-
able. It is true that, according to the laws of attrac-
tion, all bodies at an equal distance from the earth,
should fall to it in the same space of time ; and this
would actually take place if no obstacle intervened to
impede their fall. But bodies fall through the air,
and it is the resistance of the air which makes bodies
of different density fall with different degrees of ve-
locity. They must all force their way through the
36 ox THE ATTRACTION OT GRAVITY.
air, but dense heavy bodies overcome this obstacle
more easily than rarer and lighter ones.
The resistance which the air opposes to the fall of
bodies is proportioned to their surface, not to their
weight ; the air being inert, cannot exert a greater
force to support the weight of a cannon ball, than it
does to support the weight of a ball (of the same size)
made of leather ; but the cannon ball will overcome
this resistance more easily, and fall to the ground,
consequently, quicker than the leather ball.
Caroline. This is very clear, and solves the diffi-
culty perfectly. The air offers the same resistance
to a bit of lead and a bit of feather of the same size ;
yet the one seems to meet with no obstruction in its
fall, whilst the other is evidently resisted and sup-
ported for some time by the air.
Emily. The larger the surface of a body, then,
the more air it covers, and the greater is the resist-
ance it meets with from it.
Mrs. B. Certainly ; observe the manner in
which this sheet of paper falls ; it floats a while in the
air, and then gently descends to the ground. I will
roll the same piece of paper up into a ball : it offers
now but a small surface to the air, and encounters
therefore but little resistance : see how much more
rapidly it falls.
The heaviest bodies may be made to float a while
in the air, by making the extent of their surface
counterbalance their weight. Here is some gold,
which is the most dense body we are acquainted
^vith, but it has been beaten into a very thin leaf, and
offers so great an extent of surface in proportion to its
weight, that its fall, you see, is still more retarded by
the resistance of the air than that of the sheet of paper.
Caroline. That is very curious ; and it is, I sup-
pose, upon the same principle that iron boats may be
made to float on water ?
But, Mrs. B., if the air is a real body, is it not al-
so subjected to the laws of gravity ?
Mrs. B, Undoubtedly.
OxV THE ATTRACTIOX OF GRAVITY. 3V
Caroline. Then why does it not, like all other bo-
dies, fall to the ground ?
Mrs. B. On account of its spring or elasticity.
The air is an elastic Jluid ; a species of bodies, the
peculiar property of which is to resume, after com-
pression, their original dimensions ; and you must
consider the air of which the atmosphere is compo-
sed as existing in a state of compression, for its parti-
cles being drawn towards the earth by gravity, are
brought closer together than they would otherwise
be, but the spring or elasticity of the air by which it
endeavours to resist compression, gives it a constant
tendency to expand itself, so as to resume the dimen-
sions it would naturally have, if not under the influ-
ence of gravit3^ The air may therefore be said con-
stantly to struggle with the power of gravity without
being able to overcome it. Gravity thus confines the
air to the regions of our globe, whilst its elasticity
prevents it from falling like other bodies to the
ground.
Emily. The air then is, I suppose, thicker, or 1
should rather say more dense, near the surface of the
earth than in the higher regions of the atmosphere ;
for that part of the air which is nearer the surface of
the earth, must be most strongly attracted.
Mrs. B. The diminution of the force of gravity,
at so small a distance as that to which the atmosphere
extends (compared with the size of the earth) is so
inconsiderable as to be scarcely sensible ; but the
pressure of the upper parts of the atmosphere on
those beneath, renders the air near the surface of the
earth much more dense than the upper regions.
The pressure of the atmosphere has been compared
to that of a pile of fleeces of wool, in which the low-
er fleeces are pressed together by the weight of
those above ; these lie light and loose, in proportion
as they approach the uppermost fleece, which re-
ceives no external pressure, and is confined merely
by the force of its own gravity.
Caroline. It has just occurred to me that there are
4
38 ON THE ATTRACTION OF GRAVITY.
some bodies which do not gravitate towards the earth.
Smoke and steam, for instance, rise instead of falling.
Mrs. B. It is still gravity which produces their
ascent ; at least, were that power destroyed, these
bodies would not rise.
Caroline. I shall be out of conceit with gravity, if
it is so inconsistent in its operations.
Mrs. B. There is no difficulty in reconciling this
apparent inconsistency of effect. The air near the
earth is heavier than smoke, steam, or other vapours ;
it consequently not only supports 'these light bodies,
but forces them to rise, till they reach a part of the
atmosphere, the weight of which is not greater than
their own, and then they remain stationary. Look
at this basin of water ; why does the piece of paper
which I throw into it float on the surface ?
Emily. Because, being lighter than the water, it
is supported by it.
Mrs. B. And now that I pour more water into
the basin, why does the paper rise ?
Emily. The water being heavier than the paper,
gets beneath it, and obliges it to rise.
Mrs. B. In a similar manner are smoke and va-
pour forced upwards by the air ; but these bodies do
not, like the paper, ascend to the surface oi the fluid,
because, as we observed before, the air being thinner
and lighter as it is more distant from the earth, vapours
rise only till they attain a region of air of their own
density. Smoke, indeed, ascends but a very little way;
it consists of minute particles of fuel carried up by a
current of heated air from the fire below : heat, you
recollect, expands all bodies ; it consequently rarefies
air, and renders it lighter than the colder air of the
atmosphere ; the heated air from the fire carries up
with it vapour and small particles of the combustible
materials which are burning in the fire. When this
current of hot air is cooled by mixing with that of the
atmosphere, the minute particles of coal or other com-
bustible fall, and it is this which produces the small
ON THE ATTRACTION OF GRAVITY. 3d
black flakes which render the air and every thing in
contact with it, in London, so dirty.
Caroline. You must, however, allow me to make
one more objection to the universal gravity of bodies ;
which is the ascent of air balloons, the materials of
which are undoubtedly heavier than air ; how, there-
tbre, can they be supported by it ?
Mrs. B. 1 admit that the materials of which bal-
loons are made are heavier than the air; but the air
with which they are tilled is an elastic fluid, of a dif-
ferent nature from the atmospheric air, and consider-
ably lighter : so that, on the whole, the balloon is
lighter than the air which it displaces, and conse-
quently will rise, on the same principle as smoke
and vapour. Now, Emily, let me hear if you can ex-
plain how the gravity of bodies is modified by the ef-
fect of the air ?
Emily. The air forces bodies which are lighter
than itself to ascend ; those that are of an equal
weight will remain stationary in it ; and those that
are heavier will descend through it : but the air will
have some eifect on these last ; for if they are not
much heavier, they will with difficulty overcome
the resistance they meet with in passing through it,
they will be borne up by it, and their fall will be
more or less retarded.
Mrs. B. Very well. Observe how slowly this
light feather falls to the ground, while a heavier bo-
dy, like this marble, overcomes the resistance which
the air makes to its descent much more easily, and its
fall is proportionally more rapid. 1 now throw a
pebble into this tub of water ; it does not reach the
bottom near so soon as if there were no water in the
tub, because it meets with resistance from the water.
Suppose that we could empty the tub, not only of
water, but of air also, the pebble would then fall
quicker still, as it would in that case meet with no
resistance at all to counteract its gravity.
Thus you see that it is not the differe^it degrees of
gravity, but the resistance of the air, wnich prevents
40 ON THE ATTRACTION OF GRAVITY.
bodies of different weight from falling with equal ve-
locities ; if the air did not bear up the feather, it
would reach the ground as soon as the marble.
Caroline. I make no doubt that it is so ; and yet
I do not feel quite satisfied. I wish there was any
place void of air, in which the experiment could be
made.
Mrs. B. If that proof will satisfy your doubts, I
can give it you. Here is a machine called an air
punip^ (fig. 2. pi. 1.) by means of which the air may
be expelled from any close vessel which is placed
over this opening, through which the air is pumped
out. Glasses of various shapes, usually called receiv-
ers, are employed for this purpose. We shall now
exhaust the air from this tall receiver which is placed
over the opening, and we shall find that bodies of
whatever weight or size within it, will fall from the
top to the bottom in the same space of time.
Caroline. Oh, I shall be delighted with this expe-
riment! what a curious machine! how can you put
the two bodies of different weight within the glass,
without admitting the air.
Mrs. B. A guinea and a feather are already pla-
ceji there for the purpose of the experiment: here is,
you see, a contrivance to fasten them in the upper
part of the glass ; as soon as the air is pumped out, I
shall turn this little screw, by which means the brass
plates which support them will be inclined, and the
two bodies will fall. — Now 1 believe I have pretty
well exhausted the air.
Caroline. Fray let me turn the screw. — I declare,
they both reached the bottom at the same instant ?
Did you see, Emily, the feather appeared as heavy
as the guinea ?
Emily. Exactly ; and fell just as quickly. How
wonderful this is ! what a number of entertaining ex-
periments might be made with this machine I
Mrs. B. No doubt there are a great variety ; but
we shall reserve them to elucidate the subjects to
which they relate : if I had not explained to you why
ON THE ATTRACTION OP GRAVITY. 4t
the guinea and the feather fell with equal velocity,
you would not have been so well pleased with the
experiment.
Emihj. I should have been as much surprised,
but not so much interested ; besides, experiments
help to imprint on the memory the facts they are in-
tended to illustrate ; it will be better therefore for us
to restrain our curiosity, and wait for other experi-
ments in their proper places.
Caroline. Pray by what meansis the air exhaust-
ed in this receiver ?
Mrs. B. You must learn something of mechanics
in order to understand tlte construction of a pump.
At our next meeting, therefore, I shall endeavour to
make you acquainted with the law^ of motion, as an
introduction to that subject.
4*
CONVERSATION III.
ON THE LAWS OF MOTION.
Of Motion. — Of the Inertia of Bodies.— Of Force to
Produce Motion. — Direction of Motion. — Velocity,
Absolute and Relative. — Uniform Motion. — Retard-
ed Motion. — Accelerated Motion. — Velocity of Fall-
ing Bodies. — .Momentum. — Action and Re-action
Equal.— Elasticity of Bodies. — Porosity of Bodies.
— Reflected Motion. — Angles of Incidence and Re-
flection. "**-
MRS. B. The science of mechanics is founded on
the laws of motion ; it will therefore be necessary to
make you acquainted with these laws before we exa-
mine the mechanical powers. Tell me, Caroline,
what do you understand by the word motion ?
Caroline. I think I understand it perfectly, though
I am at a loss to describe it. Motion is the act of mo-
ving about, going from one place to another, it is the
contrary of remaining at rest.
Mrs. B. Very well. Motion then consists in a
change of place; a body is in motion whenever it is
changing its situation with regard to a fixed point.
Now, since we have observed that one of the general
properties of bodies is Inertia, that is, an entire pas-
siveness either with r^ard to motion or rest, it fol-
lows that a body cannot move without being put into
motion : the power which puts a body into motion is
called force ; thus the stroke of the hammer is the
ON THE LAWS OF MOTION. 43
force which drives the nail ; the pulling of the horse
that which draws the carriage, &c. Force then is
the cause which produces niotion.
Emily. And may we not sa\ that gravity is the
force which occasions the fall of bodies ?
Mrs. B. Undoubtedly. I had given you the most
familiar illustrations in order to render the explana-
tion clear ; but since you seek for more scientific
examples, you may say that cohesion is the force
which binds the particles of bodies together, and heat
that which drives them asunder.
The motion of a body acted upon by a single force
is always in a straight line, in the direction in which
it received the impulse.
Caroline. That is ver}' natural ; for as the body is
inert, and can move only because it is impelled, it
will move only in the direction in which it is impel-
led. The degree of quickness with which it moves
must, I suppose, also depend upon the degree of force
with which it is impelled.
Mrs. B. Yes ; the rate at which a body moves, or
the shortness of the time which it takes to move from
one place to another, is called its velocity ; and it is
one of the laws of motion that the velocity of the mo-
ving body is proportional to the force by which it is
put in motion. We must distinguish between abso-
lute and relative velocity.
The velocity of a body is called absolute, if we con-
sider the motion of the body in space, without any
reference to that of other bodies. When for in-
stance a horse goes fifty miles in ten hours, his velo-
city is five miles an hour.
The velocity of a body is termed relative, when
compared with that of another body which is itself in
motion. For instance, if one man walks at the rate
of a mile an hour, and another at the rate of two
miles an hour, the relative velocity of the latter is
double that of the former ; but the absolute velocity
of the one is one mile, and that of the other two
miles aa hour.
44 ON THE LAWS OF MOTION.
Emily. Let me see if 1 understand it — The rela-
tive velocity of a body is the degree of rapidity of its
motion compared with that of another body ; thus, if
one ship sail three times as far as another ship in the
same space of time, the velocity of the former is
equal to three times that of the latter.
Mrs. B. The general rule may be expressed thus :
the velocity of a body is measured by the space over
which it moves, divided by the time which it employs
in that motion : thus, if you travel one hundred miles
in twenty hours, what is your velocity in each hour ?
Emily. I must divide the space, which is one
hundred miles, by the time, which is twenty hours,
and the answer will be five miles an hour. Then,
Mrs. B., may we not reverse this rule and say, that
the time is equal to the space divided by the veloci-
ty ; since the space one hundred miles, divided by
the velocity five miles, gives twenty hours for the
time?
Mrs. B. Certainly; and we may say also that
space is equal to the velocity multiplied by the time.
Can you tell me, Caroline, how many miles you will
have travelled, if your velocity is three miles an
hour and you travel six hours ?
Caroline. Eighteen miles ; for the product of 3
multiplied by 6, is 18.
Mrs. B. I suppose that you understand what is
meant by the terms uniform^ accelerated and retarded
motion.
Emily. I conceive uniform motion to be that of a
body whose motion is regular, and at an equal rate
throughout ; for instance, a horse that goes an equal
number of miles every hour. But the hand of a
watch is a much better example, as its motion is so
regular as to indicate the time.
Mrs. B. You have a right idea of uniform motion ;
but it would be more correctly expressed by saying,
that the motion of a body is uniform w hen it passes
over equal spaces in equal times. Uniform motion is
produced by a force having acted on a body once,
ON THE LAWS OF MOTION. 46
and having ceased to act ; as ibr instance, the stroke
of a bat on a cricket ball.
Caroline. But the motion of a cricket ball is not
uniform ; its velocity gradaally diminishes till it falls
to the ground.
Mrs. B. Recollect that the cricket ball is inert,
and has no more power to stop than to put itself in
motion; if it falls, therefore, it must be stopped by
some force superior to that by which it was project-
ed, and which destroys its motion.
Caroline. And it is no doubt the force of gravity
which counteracts and destroys that of projection;
but if there were no such power as gravity, would
the cricket ball never stop?
Mrs. B. If neither gravity nor any other force,
such as the resistance of the air, opposed its motion,
the cricket ball, or even a stone thrown by the hand,
would proceed onwards in a right line, and with a
uniform velocity, for ever.
Caroline. You astonish me ! I thought that it was
impossible to produce perpetual motion ?
Mrs. B. Perpetual motion cannot be produced by
art, because gravity ultimately destroys all motion that
human powers can produce.
Emily. But independently of the force of gra-
vity, I cannot conceive that the little motion I am
capable of giving to a stone would put it in motion for
ever.
Mrs. B. The quantity of motion you communica-
ted to the stone would not influence its duration ; if
you threw it with little force it would move slowly,
for its velocity, you must remember, will be propor-
tional to the force with which it is projected ; but if
there is nothing to obstruct its passage, it will conti-
nue to move with the same velocity, and in the same
direction as when you first projected if.
Caroline. This appears to me quite incomprehen-
sible ; we do not meet with a single instance of it in na-
ture.
Mrs. B. I beg your pardon. When you come to
46 ON THE LAWS OF MOTION.
study the motion of the celestial bodies, you will llnd
that nature abounds with examples of perpetual mo-
tion ; and that it conduces as much to the harmony of
the system of the universe, as the prevalence of it
would to the destruction of all comfort on our globe.
The wisdom of Providence has therefore ordained
insurmountable obstacles to perpetual motion here
below, and though these obstacles often compel us to
contend with great difficulties, yet there results from
it that order, regularity and repose, so essential to the
preservation of all the various beings of which this
world is composed.
Now can you tell me what is retarded motion ?
Carolme. Retarded motion is that of a body which
moves every moment slower and slower ; thus when
I am tired with walking fast, I slacken my pace ; or
when a stone is thrown upweirds, its velocity is gra-
dually diminished by the power of gravity.
Mrs. B. Retarded motion is produced by some
force acting upon the body in a direction opposite to
that which lirst put it in motion : you who are an ani-
mated being, endowed with power and will, may
slacken your pace, or stop to rest when you are
tired ; but inert matter is mcapable of any feeling of
fatigue, can never slacken its pace, and never stop,
unless retarded or arrested in its course by some op-
posing force ; and as it is the laws of inert bodies
which mechanics treats of, I prefer your illustration
of the stone retarded in its ascent. Now, Emily, it is
your turn ; what is accelerated motion?
Emily. Accelerated motion, I suppose, takes
place when the velocity of a body is increased ; if
you had not objected to our giving such active bodies
as ourselves as examples, I should say that my mo-
tion is accelerated if I change my pace from walking
to running. 1 cannot think of any instance of accele-
rated motion in inanimate bodies ; all motion of inert
matter seems to be retarded by gravity.
Mrs. B. Not in all cases ; for the power of gravi-
tation sometimes produces accelerated motion ; for
ON THE LAWS OF MOTION. 47
instance, a stone falling from a height moves with a
regularly accelerated motion.
Emily. True ; because the nearer it approaches
the earth, the more it is attracted by it.
Airs. B. You have mistaken the cause of its acce-
leration of motion ; for though it is true that the force
of gravity increases as a body approaches the earth,
the difference is so trifling at any small distance from
its surface as not to be perceptible.
Accelerated motion is produced when the force
which put a body in motion continues to act upon it
during its motion, so that its motion is continually in-
creased. When a stone falls from a height, the im-
pulse which it receives from gravity during the first
instant of its fall, would be sufficient to bring it to the
ground with a uniform velocity : for, as we have ob-
served, a body having been once acted upon by a
force, will continue to move with a uniform velocity;
but the stone is not acted upon by gravity merely at
the first instant of its fall, this power continues to im-
pel it during the whole of its descent, and it is this
continued impulse which accelerates its motion.
Emily. 1 do not quite understand that.
Mrs. B. Let us suppose that the instant after you
have let fall a stone from a high tower, the force of
gravity were annihilated, the body would nevertheless
continue to move downwards, for it would have re-
ceived a first impulse from gravity, and a body once
put in motion will not stop unless it meets with some
obstacle to impede its course ; in this case its veloci-
ty would be uniform, for though there would be no
obstacle to obstruct its descent, there would be no
force to accelerate it.
Emily. That is very clear.
Mrs. B. Then you have only to add the power of
gravity constantly acting on the stone during its de-
scent, and it will not be difficult to understand that its
motion will become accelerated, since the gravity
which acts on the stone durins the first instant of its
48 ON THE LAWS OF MOTIOX.
descent, will continue in force every instant till it
reaches the ground. Let us suppose that the impulse
given by gravity to the stone during the first instant
of its descent be equal to one, the next instant we
shall find that an additional impulse gives the stone an
additional velocity equal to one, so that the accumu-
lated velocity is now equal to two ; the following in-
stant another impulse increases the velocity to three,
and so on till the stone reaches the ground.
Caroline. Now I understand it ; the effects of pre-
ceding impulses must be added to the subsequent ve-
locities.
Mrs. B. Yes ; it has been ascertained, both by
experiment and calculations, which it would be too
difficult for us to enter into, that heavy bodies de-
scending from a height, by the force of gravity, fall
sixteen feet the first second of time, three times that
distance in the next, five times in the third second,
seven times in the fourth, and so on, regularly
increasing their velocities according to the number of
seconds during which the body has been falling.
Einilij. If you throw a stone perpendicularly up-
wards, is it not the same length of time ascending that
it is descending ?
Mrs. B. Exactly ; in ascending, the velocity is di-
minished by the force of gravity ; in descending, it is
accelerated by it.
Caroline. I should then have imagined that it
would have f\dlen quicker than it rose ?
Mrs. B. You must recollect that the force with
which it is projected must be taken into the account ;
and that this force is overcome and destroyed by gra-
vity before the body falls.
Caroline. But the force of projection given to a
stone in throwing it upwards, cannot always be equal
to the force of gravity in bringing it down again, for
the force of gravity is always the same, whilst the de-
gree of impulse given to the stone is optional ; I
may throw it up gently, or with violence.
QN THE LAWS OF MOTION. 49
Mrs, B. If you throw it gently, it will not rise
high ; perhaps only sixteen feet, in which case it will
fall in one second of time. Now it is proved by ex-
periment, that an impulse requisite to project a body
sixteen ^QGi upwards, will make it ascend that height
in one second ; here then the times of the ascent and
descent are equal. But supposing it be required to
throw a stone twice that height, the force must be
proportionally greater.
You see then, that the impulse of projection in
throwing a body upwards, is always equal to the ac-
tion of the force of gravity during its descent ; and
that it is the greater or less distance to which the
body rises, that makes these two forces balance each
other.
I must now explain to you what is meant by the
momentum of bodies. It is the force, or power, with
which a body in motion strikes against another body.
The momentum of a body is composed of its quantity
of matter, multiplied by its quantity of motion; in
other words, its weight and its velocity.
Caroline. The quicker a body moves, the greater,
no doubt, must be the force with which it would strike
against another body.
Emily, Therefore a small body may have a great-
er momentum than a large one, provided its velocity
be sufficiently greater ; for instance, the momentum
of an arrow shot from a bow must be greater than a
stone thrown by the hand.
Caroline. We know also by experience, that the
heavier a body is, the greater is its force ; it is not
therefore difficult to understand, that the whole pow-
er or momentum of a body must be composed of these
two properties : but I do not understand why they
should be multiplied the one by the other ; I should
have supposed that the quantity of matter should have
been added to the quantity of motion ?
Mrs. B. It is found by experiment, that if the
weight of a body is represented by the number 3,
and its velocity also by 3, its momentum will be re-
6
50 ON THE LAWS OP MOTION,
presented by 9 ; not 6, as would be the case were
these figures added, instead of being multiplied toge-
ther. 1 recommend it to you to be careful to re-
member the definition of the momentum of bodies, as
it is one of the most important points in mechanics ;
you will find, that it is from opposing motion to mat-
ter, that machines derive their powers.*
The reaction of bodies is the next law of motion
which I must explain to you. When a body in mo-
tion strikes against another body, it meets with resist-
ance from it ; the resistance of the body at rest will
be equal to the blow struck by the body in motion ;
or, to express myself in philosophical language, action
and re-action wiW be equal, and in opposite directions.
Caroline, Do you mean to say, that the action of
the body which strikes is returned with equal force
by the body which receives the blow.
Mrs. B. Exactly.
Caroline. But if a man strikes another on the face
with his fist, he surely does not receive as much pain
by the re-action as he inflicts by the blow ?
Mrs. B. No ; but this is simply owing to the
knuckles having much less feeling than the face.
Here are two ivory balls suspended by threads,
(Plate I. fig. 3.) draw one of them, A, a little on one
side, — now let it go ; — it strikes, you see, against the
other ball B, and drives it off, to a distance equal to
that through which the first ball fell ; but the motion
of A is stopped, because when it struck B, it received
in return a blow equal to that it gave, and its motion
was consequently destroyed.
* In comparing together the momenta of different bodies, we
must be attentive to measure their weights and velocities, by the
same denomination of weights and of spaces, otherwise the re-
sults would not agree. Thus, if we estimate the weight of one
body in ounces, we must estimate the weight of the rest also in
ounces, and not in pounds ; and in computing the velocities, in
like manner, we should adhere to the same standard of measure,
both of space and of time; as for instance, the number of feet
in one second, or of mile? in one hour.
ON THE LAWS OF MOTION. 51
Emily. I should have supposed, that the motion of
the ball A was destroyed, because it had communica-
ted all its motion to B.
Mrs. B. It is perfectly true, that when one body
strikes against another, the quantity of motion com-
municated to the second body, is lost by the first ; but
this loss proceeds from the action of the body which
is struck.
Here are six ivory halls hanging in a row, (fig. 4.)
draw the first out of the perpendicular, and let it fall
against the second. None of the balls appear to
move, you see, except the last, which flies off as far
as the first ball fell ; can you explain this ?
Caroline. I believe so. When the first ball
struck the second, it received a blow in return,
which destroyed its motion ; the second ball, though it
did not appear to move, must have struck against the
third ; the re-action of which set it at rest ; the actioa
of the third ball must have been destroyed by the re-
action of the fourth, and so on, till motion was com-
municated to the last ball, which, not being re-acted
upon, flies off.
Mrs. B. Very well explained. Observe, that it
is only when bodies are elastic, as these ivory balls
are, that the stroke returned is equal to the stroke
given. I will show you the difference with these
two balls of clay, (fig. 5.) which are not elastic ;
when you raise one of these, D, out of the perpendi-
cular, and let it fall against the other, E, the re-action
of the latter, on account of its not being elastic, is not
sufficient to destroy the motion of the former ; only
part of the motion of D will be comolunicated to E,
and the two balls will move on together to d and e,
which is not to so great a distance as that through
which D fell.
Observe how useful re-action is in nature. Birds,
in flying, strike the air with their wings, and it is the
re-action of the air which enables them to rise,
or advance forw-ards ; re-action being always in a
contrary direction to action.
d2 ON THE LAWS OF MOTION.
Caroline, I thought that birds might be lighter
than the air when their wings were expanded, and
\)y that means enabled to fly.
Mrs. B. When their wings are spread, they are
better supported by the air, as they cover a greater
extent of surface ; but they are still much too heavy
to remain in that situation, without continually flap-
ping their wings, as you may have noticed, when
birds hover over their nests ; the force with which
their wings strike against the air must equal the
weight of their bodies, in order that the re-action of
the air may be able to support that weight ; the bird
will then remain stationary. If the stroke of the
wings is greater than is required merely to support
the bird, the re-action of the air will make it rise ; if
it be less, it will gently descend ; and you may have
observed the larlf, sometimes remaining with its
wings extended, but motionless ; in this state it drops
rapidly into its nest.
Caroline, What a beautiful eflect this is of the law
of re-action ! But if flying is merely a mechanical
operation, Mrs. B., why should we not construct
wings, adapted to the size of our bodies, fasten them
to our shoulders, move them with our arms, and soar
into the air.
Mrs. B. Such an experiment has been repeatedly
attempted, but never with success ; and it is now
considered as totally impracticable. The muscular
power of birds is greater in proportion to their weight
than that of man ; were we therefore furnished with
wings sufficiently large to enable us to fly, we should
not have strength to put them in motion.
In swimming, a similar action is produced on the
water, as that on the air in flying : and also in rowing ;
you strike the water with the oars, in a direction op-
posite to that in which the boat is required to move,
and it is the re-action of the water on the oars
which drives the boat along.
Emily. You said, that it was in elastic bodies only
ON THE LAWS OF MOTION. S3
that re-action was equal to action ; pray what bodies
are elastic besides the air ?
Mrs, B. In speaking of the air, I think we defined
elasticity to be a property, by means of which bodies
that are compressed return to their former state, if
I bend this cane, as soon as I leave it at liberty it re-
covers its former position ; if I press my finger upon
your arm, as soon as I remove it, the flesh, by virtue
of its elasticity, rises and destroys the impression I
made. Of all bodies, the air is the most eminent for
this property, and* it has thence obtained the name of
elastic fluid. Hard bodies are in tli€ next degree
elastic ; if two ivory, or metallic balls are struck to-
gether, the parts at which they touch will be flatten-
ed ; but their elasticity will make them instantane-
ously resume their former shape.
Caroline. But when two ivory balls strike against
each other, as they constantly do on a biUiard table, no
mark or impression is made by the stroke.
Mrs, B. I beg your pardon ; but you cannot per^
ceive any mark, because their elasticity instantly de-
stroys all trace of it.
Soft bodies, which easily retain impressions, such
as clay, wax, tallow, butter, &c. have very little elas-
ticity ; but of all descriptions of bodies liquids are the
least elastic.
Emily. If sealing-wax were elastic, instead of re-
taining the impression of a seal, it would resume a
smooth surface as soon as the weight of the seal was
removed. But pray what is it that produces the
elasticity of bodies ?
Mrs. B. There is great diversity of opinion upon
that point, and I cannot pretend to decide which ap-
proaches nearest to the truth. Elasticity implies sus-
ceptibility of compression, and the susceptibility of
compression depends upon the porosity of bodies,
for were there no pores or spaces between the par-
ticles of matter of which a body is composed, it could
not be compressed.
Caroline, That is to say, that if the particles of
6*
54 ox THE LAWS OP MOTION.
bodies were as close together as possible, they could
not be squeezed closer.
Emily. Bodies then, whose particles are most dis-
tant from each other, must be most susceptible of
compression, and consequently most elastic ; and this
you say is the case with air, which is perhaps the
least dense of all bodies ?
Mrs. B. You will not in general find this rule
hold good, for liquids have scarcely any elasticity,
whilst hard bodies are eminent for this property,
though the latter are certainly of much greater den-
sity than the former ; elasticity impHes, therefore,
not only a susceptibility of compression, but depends
upon the power of resuming its former state after
compression.
Caroline. But surely there can be no pores in
ivory and metals, Mrs. B. * how then can they be
Susceptible of compression ?
Mrs. B. The pores of such bodies are invisible to
the naked eye, but you must not thence conclude
that they have none ; it is, on the contrary, well as-
certained that gold, one of the most dense of all bo-
die!^, is extromely porous, and that these pores are
sufTiciently large to admit water when strongly com-
pressed to pass through them. This was shown by
a f -Jebrated experiment made many years ago at
Florence.
Emily. If water can pass through gold, there
must certainly be pores or interstices which afford it
a passage ; and if gold is so porous, what must other
Ijodies be, which are so much less dense than gold !
Mrs. B. The chief difference in this respect is, I
believe, that the pores in some bodies are larger thao
in others ; in cork, sponge, and bread, they form con-
liderable cavities ; in wood and stone, when not po-
lished, they are generally perceptible to the naked
eye ; whilst in ivory, metals, and all varnished and
polished bodies, they cannot be discerned. To give
you an idea of the extreme porosity of bodies, Sir
Isaac Newtoa conjectured that if the earth were so
ON THE LAWS OF MOTIOfiT. 5#
compressed as to be absolutely without pores, its
dimensions might possibly not be more than a cubic
inch.
Caroline, What an idea ! Were we not indebted
to Sir Isaac Newton for the theory of attraction, I
should be tempted to laugh at him for such a supposi-
tion. What insigniticant Httle creatures we should be J
Mrs. B. If our consequence arose from the size
of our bodies we should indeed be but pigmies, but
remember that the mind of Newton was not circum-
scribed by the dimensions of its envelope.
Emily. It is, however, fortunate that heat keeps
the pores of matter open and distended, and prevents
the attraction of cohesion from squeezing us into a
nutshell.
Mrs. B. Let us now return to the subject of re-
action, on which we have some further observations
to make. It is re-action being contrary to action
which produces reflected motion, if you throw a ball
against the wall, it rebounds ; this return of the ball
is owing to the re-action of the wall against which it
struck, and is called reflected motion.
Emily. And I now understand why balls filled with
air rebound better than those stuffed with bran or
wool; air being most susceptible of compression and
most elastic, the re-action is more complete.
Caroline. I have observed that when I throw a
ball straight against the wall, it returns straight to my
hand ; but if I throw it obliquely upwards, it rebounds
still higher, and I catch it when it falls.
Mrs. B. You should not say straight, but perpen-
dicularly against the wall ; for straight is a general
term for lines in all directions which are neither
curved nor bent, and is therefore equally applicable
to oblique or perpendicular lines.
Caroline. I thought that perpendicularly meant
either directly upwards or downwards ?
Mrs. B. In those directions lines are perpendicu-
lar to the earth. A perpendicular line has always a
reference to something towards which it is perpen-
56 ON THE LAWS OF MOTION.
dicular ; that is to say, that it inclines neither to the
one side or the other, but makes an equal angle on
every side. Do you understand what an angle is ?
Caroline. Yes, I believe so : it is two lines meet-
ing in a point.
Mrs. B. Well then, let the line A B (plate II, fig.
1.) represent the floor of the room, and the line C D
that in which you throw a ball against it ; the line C
D, you will observe, forms two angles with the line
A B, and those two angles are equal.
Emily. How can the angles be equal, while the
lines which compose them are of unequal length ?
Mrs. B. An angle is not measured by the length
of the lines, but by their opening.
Emily. Yet the longer the lines are, the greater
is the opening between them.
Mrs. B. Take a pair of compasses and draw a cir-
cle over these angles, making the angular point the
centre.
Emily. To what extent must I open the com-
passes ?
Mrs. B. You may draw the circle what size you
please, provided that its cuts the lines of the angles
we are to measure. All circles, of whatever dimen-
sions, are supposed to be divided into 360 equal parts,
called degrees ; the opening of an angle, being there-
fore a portion of a circle, must contain a certain num-
ber of degrees ; the larger the angle, the greater the
number of degrees, and two angles are said to be
»cqual when they contain an equal number of degrees.
Emily. Now 1 understand it. As the dimensions
of an angle depend upon the number of degrees con-
tained between its lines, it is the opening, and not the
length of its lines, which determines the size of the
angle.
Mrs. B. Very well : now that you have a clear
idea of the dimensions of angles, can you tell me how
many degrees are contained in the two angles formed
by one line falling perpendicularly on another, as in
the figure 1 have just drawn ?
PLATE n.
n
»
ON THE LAWS OF MOTION. 61
Emily. You must allow me to put one foot ol*
the compasses at the point of the angles, and draw a
circle round them, and then I think 1 shall be able to
answer your question : the two angles are together
just equal to half a circle, they contain therefore 90
degrees each ; 90 degrees being a quarter of 360.
Mrs. B. An angle of 90 degrees is called a right
angle, and when one line is perpendicular to another,
it forms, you see, (fig. 1.) a right angle on either
side. Angles containing more than 90 degrees are
called obtuse angles ; (fig. 2.) and those containing
less than 90 degrees are called acute angles, (fig. 3.)
Caroline. The angles of this square table are right
angles, but those of the octagon table are obtuse an-
gles ; and the angles of sharp-pointed instruments are
acute angles.
Mrs. B. Very well. To retarn now to your ob-
servation, that if a ball is thrown obliquely against
the wall it will not rebound in the same direction ;
tell me, have you ever played at billiards ?
Caroline, Yes, frequently ; and I have observed
that when I push the ball perpendicularly against the
cushion, it returns in the same direction ; but when
I send it obliquely to the cushion, it rebounds ob-
liquely, but on the opposite side ; the ball in this lat-
ter case describes an angle, the point of which is at
the cushion. I have observed too, that the more ob-
liquely the ball is struck against the cushion, the
more obliquely it rebounds on the opposite side, so
that a billiard player can calculate with great accu-
racy in what direction it will return.
Mrs. B. Very well. This figure (fig. 4. plate II.)
represents a billiard table ; now if you draw a line
A B from the point where the ball A strikes perpen-
dicular to the cushion ; you will find that it will di-
vide the angle which the ball describes into two parts,
or two angles ; the one will show the obliquity of the
direction of the ball in its passage towards the cush-
ion, the other its obliquity in its passage back from
the cushion. The first is called the angle of inci-
58 ON THE LAWS OF MOTION.
dence^ the other the angle of reflection, and these ao-
gles are always equal.
Caroline. This then is the reason why, when I
throw a ball obliquely against the wall, it rebounds in
an opposite oblique direction, forming equal angles of
incidence and of reflection.
Mrs, B. Certainly ; and you will find that the
more obliquely you throw the ball, the more oblique-
ly it will rebound.
We must now conclude ; but I shall have some
further observations to make upon the laws of mo-
tion, at our next meeting.
CONVERSATION IV.
ON COxMPOUND MOTION.
Compound Motion, the Result of two Opposite For-
ces.— Of Circular Motion, the Result of two Forces,
one of which confines the Body to a Fixed Point. —
Centre of Motion, the Point at Rest while the other
Parts of the Body move round it. — Centre of Magni-
tude, the Middle of a Body. — Centripetal Force, that
which confines a Body to a fixed Central Point. —
Centrifugal Force, that which impels a Body to fly
from the Centre. — Fall of Bodies in a Parabola. —
Centre of Gravity, the Centre of Weight, or point
about which the Parts balance each other,
MRS. B. I must explain to you the nature of com-
pound motion. Let us suppose a body to be struck
by two equal forces in opposite directions, how will
it move ?
Emily. If the directions of the forces are in exact
opposition to each other, I suppose the body would
not move at all.
Mrs. B. You are perfectly right ; but if the for-
ces, instead of acting on the body in opposition, strike
it in two directions inclined to each other, at an angle
of ninety degrees, if the ball A (fig. 6. plate II.) be
struck by equal forces at X and at Y, will it not
move ?
Emily. The force X would send it towards ,B, and
the force Y towards C ; and since these forces are
equal, I do not know how the body can obey one im^
pulse rather than the other, and yet I think the ball
60 ON COMPOUND MOTION.
would move, because, as the two forces do not act in
direct opposition, they cannot entirely destroy the
effect of each other.
Mrs, B, Very true ; the ball will therefore follow
the direction of neither of the forces, but will move
in a line between them, and will reach D in the same
space of time, that the force X would have sent it to
B, and the force Y would have sent it to C. Now, if
you draw two lines from D, to join B and^, you will
form a square, and the oblique line which the body
describes is called the diagonal of the square.
Caroline. That is very clear, but supposing the
two forces to be unequal, that the force X, for in*
stance, be twice as great as the force Y ?
Mrs. B. Then the force X would drive the ball
twice as far as the force Y, consequently you must
draw the line A B (fig. 6.) twice as long as the line
A C, the body will in this case move to D ; and if
you draw lines from that point to B rand C, you will
iind that the ball has moved in the diagonal of a
rectangle.
Emily. Allow me to put another case ? Suppose
the two forces are unequal, but do not act on the ball
in the direction of a right angle, 'but in that of an
acute angle, what will result ?
Mrs. B. Prolong the lines in the directions of the
two forces, and you will soon discover which way the
ball will be impelled ; it will move from A to D, in the
diagonal of a parallelogram, (fig. 7.) Forces acting
in the direction of lines forming an obtuse angle, will
also produce motion in the diagonal of a parallel-
ogram. For instance, if the body set out from B,
instead of A, and was impelled by the forces X and
Y, it would move in the dotted diagonal B C.
We may now proceed to circular motion : this is
the result of two forces on a body, by one of which
it is projected forward in a right line, whilst by the
other it is confined to a fixed point. For instance,
when 1 whirl this ball, which is fastened to ray hand
with a string, the ball moves in a circular direction ;
ON COMPOUND MOTION. 01
because it is acted on by two forces, that which I
give it, which represents the force of projection, and
that of the string, which confines it to my hand. If
during its motion you were suddenly to cut the string,
the ball would fly off in a straight line ; being releas-
ed from confinement to the fixed point, it would be
acted on but by one force, and motion produced by
one force, you know, is always in a right hne.
Caroline. This is a little more difficult to compre-
hend than compound motion in straight hnes.
Mrs. B. You have seen a mop trundled, and have
observed that the threads which compose the head
-of the mop fly from the centre ; but being confined
to it at one end, they cannot part from it ; whilst the
water they contain, being unconfined, is thrown off in
straight lines.
Emily. In the same way, the flyers of a windmill,
when put in motion by the wind, would be driven
straight forwards in a right line, were they not con-
fined to a fixed point, round which they are compel-
led to move.
Mrs. B. Very well. And observe, that the point
to which the motion of a small body, such as the ball
with the string, which may be considered as revolv-
ing in one plane, is confined, becomes the centre of
its motion. But when the bodies are not of a size or
shape to allow of our considering every part of them
as moving in the same plane, they in reality revolvje
round a line, which line is called the axis of motion.
In a top, for instance, when spinning on its point, the
axis is the line which passes through the middle of it,
perpendicularly to the floor.
Caroline. The axle of the flyers of the windmill
is then the axis of its motion ; but is the centre of
motion always in the middle of a body ?
Mrs. B. No, not always. The middle point of a
body is called its centre of magnitude, or position,
that is, the centre of its mass or bulk. Bodies have
also another centre, called the centre of gravity,
»y}iich I shall explain to you ; but at present, we must
62 ON COMPOUND MOTION.
confine ourselves to the axis of motion. This line
you must observe remains at rest, whilst all the other
parts of the body move around it ; when you spin a
top the axis is stationary whilst every other part is in
motion round it.
Caroline. But a top generally has a motion for-
wards, besides its spinning motion ; and then no point
within it can be at rest ?
Mrs. B. What i say of the axis of motion, relates
only to circular motion ; that is to say, to motion
round a line, and not to that which a body may have
at the same time in any other direction. There is
one circumstance in circular motion, which you must
carefully attend to ; which is, that the further any
part of a body is from the axis of motion, the greater
is its velocity ; as you approach that line, the velo-
city of the parts gradually diminishes till you reach the
axis of motion, which is perfectly at rest.
Caroline. But, if every part of the same body did
not move with the same velocity, that part which
moved quickest must be separated from the rest of
the body, and leave it behind ? ^
Mrs. B. You perplexyourself by confounding the
idea of circular motion with that of motion in a right
line : you must think only of the motion of a body
round a fixed line, and you will find, that if the parts
farthest from the centre had not the greatest velocity,
those parts would not be able to keep up with the
rest of the body, and would be left behind. Do not
the extremities of the vanes of a windmill move over
a much greater space, than the parts nearest the axis
of motion ? (plate III. fig. 1.) the three dotted circles
describe the paths in which three different parts of
the vanes move, and though the circles are of diff'er-
ent dimensions, the vanes describe each of them in
the same space of time.
Caroline. Certainly they do ; and I now only won-
der, that we neither of us ever made the observation
before : and the same effect must take place in a so-
lid body, like the top, in spinning ; the most bulging
%■ ^■
PLATE n
Fi^S.
Fi^.4
%• '^■
Fi^. S.
F^ 8
ON COxMPOUND MOTION. 63
part of the surface must move with the greatest rapi-
dfty.
Mrs. B. The force which confines a body to a
centre round which it moves is called the centripetal
force ; and that force, which impels a body to fly
from the centre, is called the centrifugal force ; in
circular motion, these two forces constantly balance
each other : otherwise the revolving body would ei-
ther approach the centre, or recede from it, accord-
ing as the one or the other prevailed.
Caroline. When I see any body moving in a circle,
I shall remember that it is acted on by two forces.
Mrs. B. Motion, either in a circle, an ellipsis, or
any other curve-line, must be the result of the action
of two forces ; for you know, that the impulse of one
single force always produces motion in a right line.
Emily. And if any cause should destroy the cen-
tripetal force, the centrifugal force would alone im-
pel the body, and it would I suppose fly off in a
straight line from the centre to which it had been
confined.
Mrs. B. It would not fly off" in a right line from
the centre ; but in a right line in the direction in
which it was moving, at the instant of its release ; if a
stone, whirled round in a sling, gets loose at the
point A, (plate III. fig. 2.) it flies off in the direction
A B ; this Hne is called a tangent, it touches the cir-
cumference of the circle, and forms a right angle
with a line drawn from that point of the circumfer-
ence to the centre of the circle, C.
Emily. You say, that motion in a curve-line is
owing to two forces acting upon a body ; but when 1
throw this ball in a horizontal direction, it describes
a curve-line in falling ; and yet it is only acted upon
by the force of projection ; there is no centripetal
force to confine it, or produce compound motion.
Mrs. B. A ball thus thrown, is acted upon by no
less than three forces ; the force of projection, which
you communicated to it ; the resistance of the air
through which it passes, which diminishes its veloci-
04 ON COMPOUND MOTION.
ty, without changing its direction ; and the force of
gravit}^ which finally brings it to the ground. The
power of gravity, and the resistance of the air, being
always greater than any force of projection we can
give a body, the lattdr is gradually overcome, and the
body brought to the ground ; but the stronger the
projectile force, the longer will these powers be in
subduing it, and the further the body will go before it
falls.
Caroline. A shot fired from a cannon, for instance,
will go much further than a stone projected by the
hand.
Mrs. B. Bodies thus projected, you observed,
described a curve-line in their descent; can you ac-
' count for that?
Caroline. No ; I do not understand why it should
not fall in the diagonal of a square.
Mrs. B. You must consider that the force of pro-
jection is strongest when the ball is first thrown ; this
force, as it proceeds, being weakened by the continued
resistance of the air, the stone, therefore, begins by
moving in a horizontal direction ; but as the strong-
er powers prevail, the direction of the ball will gradu-
ally change from a horizontal to a perpendicular
line. Projection alone, would drive the ball A, to B,
(fig. 3.) gravity would bring it to C ; therefore, when
acted on in different directions, by these two forces,
it moves between, gradually inclining more and more
to the force of gravity, in proportion as this accumu-
lates ; instead therefore of reaching the ground at D,
as you supposed it would, it falls somewhere about E.
Caroline. It is precisely so ; look, Emily, as I
throw this ball directly upwards, how the resistance
of the air and gravity conquers projection. Now I
will throw it upwards obliquely ; see, the force of
projection enables it, for an instant, to act in opposi-
tion to that of gravity ; but it is soon brought down
again.
Mrs. B. The curve-line which the ball has de-
scribed, is called in geometry r parabola ; but when
ON COMPOUND MOTION. Qo
the ball is thrown perpendicularly upwards, it will
descend perpendicularly ; because the force of pro-
jection, and that of gravity, are in the same line of
direction.
We have noticed the centres of magnitude, and of
motion ; but I have not yet explained to you what is
meant by the centre of gravity ; it is that point in a
body, about which all the parts exactly balance each
other ; if therefore that point is supported, the body
will not fall. Do you understand this ?
Emily. I think so, if the parts round about this
point have an equal tendency to fall, they will be in
equilibrium, and as long as this point is supported,
the body cannot fall.
Mrs. B. Caroline, what would be the effect, were
any other point of the body alone supported ?
Caroline. The surrounding parts no longer balan-
cing each other, the body, I suppose, would fall on
the side at which the parts are heaviest.
Mrs. B. Infallibly; whenever the centre ofgra
vity is unsupported the body must fall. This some-
times happens with an overloaded wagon winding up
a steep hill, one side of the road being more elevated
than the other ; let us suppose it to slope as is de-
scribed in this figure, (plate III. fig. 4.,) we will say,
that the centre of gravity of this loaded wagon is at
the point A. Now your eye will tell you, that a wa-
gon thus situated will overset ; and the reason is,
that the centre of gravity A, is not supported ; for if
you draw a perpendicular line from it to the ground
at C, it does not fall under the wagon within the
wheels, and is therefore not supported by them.
Caroline. I understand that perfectly ; but what
is the meaning of the other point B ?
Mre. B. Let us, in imagination, take off the upper
part of the load ; the centre of gravity will then
change its situation, and descend to B, as that will
now be the point about which the parts of the less
heavily laden wagon will balance each other. Will
the wagon now be upset?
6*
G.6 ON COMPOUND MOTION.
Caroline. No, because a perpendicular line from
that point falls within the wheels at D, and is support-
ed by them ; and when the centre of gravity is sup-
ported, the body will not fall.
Emily, Yet I should not much like to pass a wa-
gon in that situation ; for, as you see, the point D is
but just within the left wheel ; if the right wheel was
merely raised, by passing over a stone, the point D
would be thrown on the outside of the left wheel, and
the wagon would upset.
Caroline. A wagon, or any carriage whatever,
will then be most firmly supported, when the centre
of gravity falls exactly between the wheels ; and that
is the case in a level road.
Pray, whereabouts is the centre of gravity of the
human body ?
Mrs. B. Between the hips ; and as long as we
Stand upright, this point is supported by the feet ; if
you lean on one side, you will find that you no longer
stand firm. A rope-dancer performs all his feats of
agility, by dexterously supporting his centre of gravi-
ty ; whenever he finds that he is in danger of
losing his balance, he shifts the heavy pole, which be
holds in his hands, in order to throw the weight
towards the side that is deficient ; and thus, by chang-
ing the situation of the centre of gravity, he restores
his equilibrium.
Caroline. When a stick is poised on the tip of the
finger, is it not by supporting its centre of gravity ?
Mrs. B. Yes ; and it is because the centre of gra-
vity is not supported that spherical bodies roll down
aslope. A sphere, being perfectly round, can touch
the slope but by a single point, and that point cannot
be perpendicularly under the centre of gravity, and
therefore cannot be supported, as you will perceive
by examining this figure. (Fig. 5. plate III.)
Emily. So it appears ; yet I have seen a cylinder
of wood roll up a slope ; how is that contrived ?
Mrs. B. It is done by plugging one side of the
i^y Under with lead, as at B, (fig. 5» plate III.) the bo-
ON COMPOUND MOTION. 6?
dy being no longer of a uniform density, the centre of
gravity is removed from the middle of the body to
some point in the lead, as that substance is much hea-
vier than wo«d ; now you may observe that in order
that the cylinder may roll down the plane, as it is
here situated, the centre of gravity must rise, which
is impossible ; the centre of gravity must always de-
scend in moving, and will descend by the nearest and
readiest means, which will be by forcing the cylinder
up the slope, until the centre of gravity is supported,
and then it stops.
Caroline. The centre of gravity, therefore, is not
always in the middle of a body ?
Mrs. B. No, that point we have called the centre
of magnitude; when the body is of a uniform densi-
ty, the centre of gravity is in the same point; but
when one part of the body is composed of heavier
materials than another part, the centre of gravity be-
ing the centre of the weight of the body can no long-
er correspond with the centre of magnitude. Thus
you see the centre of gravity of this cylinder plugged
with lead, cannot be in the same spot as the centre of
magnitude.
Emily. Bodies, therefore, consisting but of one
kind of substance, as wood, stone, or lead, and whose
densities are consequently uniform, must stand more
firmly, and be more difficult to overset, than bodies
composed of a variety of substances^ of different den-
sities, which may throw the centre of gravity on one
side.
Mrs. B. Yes ; but there is another circumstance
which more materially affects the firmness of their
position, and that is their form. Bodies that have a
narrow base are easily upset, for if they are the least
inclined, their centre is no longer supported, as you
may perceive in fig. 6.
Caroline. I have often observed with what diffi-
culty a person carries a single pail of water ; it is
owing, I suppose, to the centre of gravity being
thrown on one side, and the opposite arm is stretched
68 ON COMPOUND MOTION.
out to endeavour to bring it back to it3 original situa-
tion ; but a pail hanging on each arm is carried with-
out difficulty, because they balance each other, and
the centre of gravity remains supported by the feet.
Mrs. B. Very well ; 1 have but one more remark
to make on the centre of gravity, which is, that when
two bodies are fastened together, by a line, string,
chain, or any power whatever, they are to be consi-
dered as forming but one body ; if the two bodies be
of equal weight, the centre of gravity will be in the
middle of the line which unites them, (fig. 7.) but if
one be heavier than the other, the centre of gravity
will be proportionally nearer the heavy body than the
light one. (fig. 8.) If you were to carry a rod or
pole with an equal weight fastened at each end of it,
you would hold it in the middle of the rod, in order
that the weights should balance each other ; whilst if
it had unequal weights at each end, you would hold
it nearest the greater weight, to make them balance
each other.
Emily. And in both cases we should support the
centre of gravity ; and if one weight be very consi-
derably larger than the other, the centre of gravity
will be thrown out of the rod into the heaviest weight.
(fig. 9.)
Mrs. B. Undoubtedlv.
CONVERSATION V.
ON THE MECHANICAL POWERS.
Of the Power of Machines. — Of the Lever in General.
— Of the Lever of the First Kind, having the Fulcrum
between the Power and the Weight. — Of the Lever of
the Second Kind, having the Weight between the Pow-
er and the Fulcrum. — Of the Lever of the Third Kindy
having the Power between the Fulcrum and the
Weight.
MRS. B. We may now proceed to examine the
mechanical powers ; they are six in number, one or
more of which enters into the composition of every
machine. The lever, the pulley, the wheel, and axle^
the inclined plane, the wedge, and the screw.
In order to understand the power of a machine,
there are four things to be considered. 1st. The
power that acts : this consists in the effort of men or
horses, of weights, springs, steam, &c.
2dly. The resistance which is to be overcome by
the power ; this is generally a weight to be moved.
The power must always be superior to the resist-
ance, otherwise the machine could not be put in mo-
tion.
Caroline. If for instance the resistance of a car-
riage was greater than the strength of the horses
employed to draw it, they would not be able to make
it move.
Mrs, B, 3dly. We are to consider the centre of mo~
TO ON THE MECHANICAL POWERS.
tion, or, as it is termed in mechanics, the fulcrum;
this you may recollect is the point about which all
the parts of the body move; and, lastly, the respective
velocities of the power, and of the resistance.
Emily. That must depend upon their respective
distances from the axis of motion ; as we observed in
the motion of the vanes of the windmill.
Mrs. B. We shall now examine the power of the
lever. The lever is an inflexible rod or beam of any
kind, that is to say, one which will not bend in any
direction. For instance, the steel rod to which these
scales are suspended is a lever, and the point in
which it is supported the fulcrum, or centre of mo-
tion ; now, can you tell me why the two scales are
in equilibrium ?
Caroline. Being both empty, and of the same
weight, they balance each other.
Emily. Or, more correctly speaking, because the
centre of gravity common to both is supported.
Mrs. B. Very well ; and which is the centre of
gravity of this pair of scales ? (fig. 1. plate III.)
Emily. You have told us that when two bodies of
equal weight were fastened together, the centre of
gravity was in the middle of the line that connected
them ; the centre of gravity of the scales must there-
fore be in the fulcrum F of the lever which unites
the two scales ; and corresponds with the centre of
motion.
Caroline. But if the scales contained different
weights, the centre of gravity would no longer be in
the fulcrum of the lever, but removed towards that
scale which contained the heaviest weight ; and since
that point would no longer be supported, the heavy
scale would descend and outweigh the other.
Mrs. B. True ; but tell me, can you imagine any
mode by which bodies of different weights can be
made to balance each other, either in a pair of scales,
or simply suspended to the extremities of the lever ?
for the scales are not an essential part of the machine,
they have no mechanical power, and are used merely
PLATu nr
ON THE MECHANICAL POWERS. 71
for the convenience of containing the substance to
be weighed.
Caroline. What! make a light body balance a
heavy one ? I cannot conceive that possible.
Mrs. B. The fulcrum of this pair of scales (fig.
2.) is moveable, you see ; I can take it ofif the prop,
and fiisten it on again in another part ; this part is
now become the fulcrum, but it is no longer in the
centre of the lever.
Caroline. And the scales are no longer true ; for
that which hangs on the longest side of the lever de-
scends.
Mrs. B. The two parts of the lever divided by
the fulcrum are called its arms, you should therefore
say the longest arm, not the longest side of the lever.
These arms are likewise frequently distinguished
by the appellations of the acting and the resisting
part of the lever.
Your observation is true that the balance is now
destroyed ; but it will answer the purpose of en-
abling you to comprehend the power of a lever when
the fulcrum is not in the centre.
Emily. This would be an excellent contrivance
for those who cheat in the weight of their goods ; by
making the fulcrum a little on one side, and placing the
goods in the scale which is suspended to the longest
arm of the lever, they would 4ippear to weigh more
than they do in reality.
Mrs. B. You do not consider how easily the fraud
would be detected ; for on the scales being emptied
they would not hang in equilibrium.
Emily. True ; I did not think of that circum-
stance. But I do not understand why the longest arm
of the lever should not be in equilibrium with the
other ?
Caroline. It is because it is heavier than the short-
est arm ; the centre of gravity, therefore, is no long-
er supported.
Mrs. B. You are right ; the fulcrum is no longer
in the centre of gravity ; but if we can contrive to
72 ON THE MECHANICAL POWERS.
make the fulcrum in its present situation become the
centre of gravity, the scales will again balance each
other ; for you recollect that the centre of gravity is
that point about which every part of the body is in
equilibrium.
Emily. It has just occurred to me how this may
be accomplished ; put a great weight into the scale
suspended to the shortest arm of the lever, and a
smaller one into that suspended to the longest arm.
Yes, 1 have discovered it — look, Mrs. B., the scale
on the shortest arm will carry 21bs., and that on the
longest arm only one, to restore the balance, (tig. 3.)
Mrs. B. You see, therefore, that it is not so im-
practicable as you imagined to make a heavy body
balance a light one ; and this is in fact the means by
which you thought an imposition in the weight of
goods might.be effected, as a weight often or
twelve ounces might thus be made to balance a pound
of goods. Let us now take off the scales, that we
may consider the lever simply ; and in this state you
see that the fulcrum is no longer the centre of gravi-
ty ; but it is, and must ever be, the centre of motion,
as it is the only point which remains at rest, while
the other parts move about it.
Caroline. It now resembles the two opposite vanes
of a windmill, and the fulcrum the point round which
they move.
Mrs. B. In describing the motion of those vanes,
you may recollect our observing that the farther a
body is from the axis of motion the greater is its
velocity.
Caroline. That I remember and understood per-
fectly.
Mrs. B. You comprehend then, that the extremi-
ty of the longest arm of a lever must move with
greater velocity than that of the shortest arm ?
Emily. No doubt, because it is farthest from the
centre of motion. And pray, Mrs. B., when my
brothers play at see-saw, is not the plank on which
they ride a kind of lever ?
UN THE MECHANICAL POWERS. 73
Mrs, B. Certainly ; the log of wood which sup-
ports it from the ground is the fulcrum, and those who
ride represent the power and the resistance at each
end of the lever. And have you not observed that
when those who ride are of equal weight, the plank
must be supported in the middle to make the two
arms equal ; whilst, if the persons diifer in weight,
the plank must be drawn a little further over the prop,
.>, make the arms unequal, and the lightest person,
who represents the resistance, must be placed at the
extremity of the longest arm.
Caroline. That is always the case when I ride on
a plank with my youngest brother; 1 have observed also
that the lightest person has the best ride, as he moves
both further and quicker ; and I now understand that
it is because he is more distant from the centre of
motion.
Mrs. B. The greater velocity with which your
little brother moves, renders his momentum equal to
yours.
Caroline. Yes ; I have the most gravity, he the
greatest velocity ; so that upon the whole our mo-
mentums are equal. — But you said, Mrs. B., that the
power should be greater than the resistance to put
the machine in motion ; how then can the plank
move if the momentums of the persons who ride are
equal.
Mrs. B. Because each person at his descent
touches the ground with his feet ; the reaction of
which gives him an impulse which increases his ve-
locity ; this spring is requisite to destroy the equili-
brium of the power and the resistance, otherwise,
the plank would not move. Did you ever observe
that a lever describes the arc of a circle in its motion?
Emily. No ; it appears to me to rise and descend
perpendicularly ; at least I always thought so.
Mrs. B. I believe I must make a sketch of you
and your brother riding on a plank, in order to con-
vince you of your error, (fig. 4. pi. IV.) You may
now observe that a lever can move only round the
7
74 ON THE MECHANICAL POWERS.
fulcrum, since that is the centre of motion ; it would,
be impossible for you to rise perpendicularly to the
point A, or for your brother to descend in a straight
line to the point B ; yon must in rising and he in de-
scending describe arcs of your respective circles.
This drawing shows you also how much superior his
velocity must be to yours ; for if you could swing
quite round, you would each complete your respec-
tive circles in the same time.
Caroline. My brother's circle being much the
largest, he must undoubtedly move the quickest.
Mrs. B. Now tell me, do you think that your
brother could raise you as easily without the aid of a
lever?
Caroline. Oh no, he could not lift me off the
ground.
Mrs. B. Then 1 think you require no further
proof of the power of a lever, since you see what it
enables your brother to perform.
Caroline, I now understand what you meant by
saying, that in mechanics motion was opposed to mat-
ter, for it is my brother's velocity w|iich overcomes
my weight.
Mrs. B. You may easily imagine what enormous
weights may be raised by levers of this description,
for the longer the acting part of the lever in compari-
son to the resisting part, the greater is the effect pro-
duced by it ; because the greater is the velocity of
the power compared to that of the weight.
There are three different kinds of levers; in the
first the fulcrum is between the power and the weight.
Caroline. This kind then comprehends the seve-
ral levers you have described.
Mrs. B. Yes, when in levers of the first kind, the
fulcrum is equally between the power and the weight,
as in the balance the power must be greater than the
weight, in order to move it ; for nothing can in this
case be gained by velocity ; the two arms of the le-
ver being equal, the velocity of their extremities
must be so likewise. The balance is therefore of no
ON THE MECHANICAL POWERS. iO
assistance as a mechanical power, but it is extremely
tiseful to estimate the respective weights of bodies.
But when (fig. 6.) the fulcrum F of a lever is not
equally distant from the power and the weight, and
that the power P acts at the extremity of the longest
arm, it may be less than the weight W, its deficiency
being compensated by its superior velocity ; as we
observed in the sce-saw.
Emily. Then when we want to lift a great weight,
we must fasten it to the shortest arm of a lever, and
apply our strength to the longest arm ?
Mrs. B. If the case will admit of your putting
the end of the lever under the weight, no fastening
will be required ; as you will perceive by stirring the
fire.
Emily. Oh yes! the poker is a lever of the first
kind, the point where it rests against the bars of the
grate, whilst I am stirring the fire, is the fulcrum ; the
short arm, or resisting part of the lever, is employed
in lifting the weight, which is the coals, and my hand
is the power applied to the longest arm, or acting part
of the lever.
Mrs. B. Let me hear, Caroline, whether you can
equally well explain this instrument, which is compos-
ed of two levers, united in one common fulcrum.
Caroline. A pair of scissars !
Mrs. B. You are surprised, but if you examine
their construction, you will discover that it is the
power of the lever that assists us in cutting with scis-
sars.
Caroline. Yes ; I now perceive that the point at
which the two levers are screwed together, is the
fulcrum ; the handles, to which the power of the fin-
gers is applied, are the extremities of the acting part
of the levers, and the cutting part of the scissars are
the resisting parts of the levers : therefore, the long-
er the handles and the shorter the points of the scis-
sars, the more easily yon cut with them.
Emily. That I have often observed, for when I
cut paste-board or any hard substance, I always make
76 ox THE MECHANICAL POWERS.
use of that part of the scissars nearest the screw or
rivet, and J now understand why it increases the pow-
er of cutting; hut I confess that I never should have
discovered scissars to have been double levers ; and
pray are not snuffers levers of a similar description ?
Mrs. B. Yes, and most kinds of pincers ; the
great power of which consists in the resisting part of
the lever being very short in comparison of the acting
part.
Caroline. And of what nature are the two other
kinds of levers ?
Mrs. B. In levers of the second kind, the weight,
instead of being at one end, is situated between the
power and the fulcrum, (fig. 6.)
Caroline. The weight and the fulcrum have here
changed places ; and what advantage is gained by this
kind of lever ?
Mrs. B. In moving it, the velocity of the power
must necessarily be greater than that of the weight,
as it is more distant from the centre of the motion.
Have you ever seen your brother move a snow-ball
by means of a strong stick, when it became too heavy
for him to move without assistance ?
Caroline. Oh yes ; and this was a lever of the se-
cond order ; (fig. 7.) the end of the stick, which he
thrusts under the ball, and which rests on the ground,
becomes the fulcrum ; the ball is the weight to be
moved, and the power his hands applied to the other
end of the lever. In this instance there is an immense
difference in the length of the arms of the lever ; for
the weight is almost close to the fulcrum.
Mrs. B. And the advantage gained is proportional
to this difference. Fishermen's boats are by levers
of this description raised from the ground to be
launched into the sea, by means of slippery pieces of
board which are thrust under the keel. The most
common example that we have of levers of the second
kind is in the doors of our apartments.
Emily. The hinges represent the fulcrum, oiir
ON THE MECHANICAL POWERS. 77
hands the power applied to the other end of the lever ;
but where is the weight to be moved ?
Mrs. B. The door is the weight, and it conse-
quently occupies the whole of the space between the
power and the fulcrum. Nutcrackers are double le-
vers of this kind : the hinge is the fulcrum, the nut
the resistance, and the hands the power.
In levers of the third kind (fig. 8.), the fulcrum is
again at one of the extremities, the weight or resist-
ance at the other, and it is now the power which is
applied between the fulcrum and the resistance.
Emily. The fulcrum, the weight, and the power,
then, each in their turn, occupy some part of the
middle of the lever between its extremities. But in
this third kind of lever, the weight being farther from
the centre of motion than the power, the difficulty of
raising it seems increased rather than diminished.
Mrs. B. That is very true ; a lever of this kind is
therefore never used, unless absolutely necessary,
as is the case in lifting up a ladder perpendicularly in
order to place it against a wall ; the man who raises
it cannot place his hands on the upper part of the
ladder, the power, therefore, is necessarily placed
much nearer the fulcrum than the weight.
Caroline, Yes, the hands are the power, the
ground the fulcrum, and the upper part of the ladder
the weight.
Mrs. B. Nature employs this kind of lever in the
structure of the human frame. In lifting a weight
with the hand, the lower part of the arm becomes a
lever of the third kind ; the elbow is the fulcrum, the
muscles of the fleshy part of the arm the power ; and
as these are nearer to the elbow than the hand, it is
necessary that their power should exceed the weight
to be raised.
Emily. Is it not surprising that nature should have
furnished us with such disadvantageous levers ?
Mrs. B, The disadvantage, in respect to power,
is more than counterbalanced by the convenience re-
sulting from this structure of the arm j and it is no
7*.
78 ON THE MECHANICAL POWERS,
doubt that which is best adapted to enable it to per-
form its various functions.
We have dwelt so long on the lever, that we must
reserve the examination of the other mechanical pow-
ers to our next interview.
^^'
Fich 2.
PLATE V.
Awrv^x
CONVERSATION VL
ON THE MECHANICAL POWERS.
Of the Pulley.^Of the Wheel arid Axle.— Of the In-
clined Plane. — Of the Wedge. — Of the Screw.
MRS. B. The pulley is the second mechanical
power we 'are to examine. You both, I suppose,
have seen a pulley ?
Caroline. Yes, frequently : it is a circular and
flat piece of wood or metal, with a string which runs
in a groove round it ; by means of which a weight
may be pulled up ; thus pulleys are used for drawing
up curtains.
Mrs. B. Yes ; but in that instance the pulleys
are fixed, and do not increase the power to raise the
weights, as you will perceive by this figure, (plate V.
fig 1.) Observe that the fixed pulley is on the same
principle as the lever of a pair of scales, in which
the fulcrum F being in the centre of gravity, the
power P and the weight W, are equally distant from
it, and no advantage is gained.
Emily. Certainly ; if P represents the power em-
ployed to raise" the weight W, the power must be
greater than the weight in order to move it. But of
what use then are pulleys in mechanics ?
Mrs. B. The next figure represents a pulley
which is not fixed, (fig. 2.) and thus situated you will
perceive that it affords us mechanical assistance. In
order to raise the weight (W) one inch, P, the pow-
80 ON THE MECHANICAL POWERS.
er, must draw the strings B and C one inch each ;
the whole string is therefore shortened two inches,
while the weight is raised only one.
Emily. That I understand : if P drew the string
but one inch, the weight would be raised only half
an inch, because it would shorten the strings B and
C half an inch each, and consequently the pulley,
with the weight attached to it, can be raised only
half an inch.
Caroline. I am ashamed of my stupidity ; but I
confess that I do not understand this ; it appears to
me that the weight would be raised as much as the
string is shortened by the power.
Mrs. B. I will endeavour to explain it more
clearly. I fasten this string to a chair and draw it
towards me ; I have now shortened the string, by
the act of drawing it, one yard.
Caroline. And the chair, as I supposed, has ad-
vanced one yard.
Mrs. B. This exemplifies the nature of a single
^xed pulley only. Now unfasten the string, and re-
place the chair where it stood before. In order to
represent the moveable pulley, we must draw the
chair forwards by putting the string round it ; one
end of the string may be fastened to the leg of the
table, and I shall draw the chair by the other end of
the string. I have again shortened the string one
yard ; how much has the chair advanced ?
Caroline. I now understand it ; the chair repre-
sents the weight to which the moveable pulley is at-
tached ; and it is very clear that the weight can be
drawn only half the length you draw the string. I
believe the circumstance that perplexed me was, that
1 did not observe the difference that results from the
weight being attached to the pulley, instead of being
fastened to the string, as is the case in the fixed pul-
ley.
Emily. But I do not yet understand the advantage
of pulleys ; they seem to me to increase rather than
diminish the difficulty of raising weights, since you
ON THE MECHANICAL POWERS. 81
must draw the string double the length that you
raise the weighty whilst with a single pulley, or
without any pulley, the weight is raised as much as
the string is shortened.
J^lrs. B. The advantage of a moveable pulley
consists in dividing the difficulty ; we must draw, it
is true, twice the length of the string, but then only
half the strength is required that would be necessary
to raise the weight without the assistance of a move-
able pulley.
Emily. So that the difficulty is overcome in the
same manner as it would be, by dividing the weight
into two equal parts, and raising them successively.
Mrs. B. Exactly. You must observe, that with
a moveable pulley the velocity of the power is double
that of the weight, since the power P (fig. 2.) moves
two inches whilst the weight W moves one inch ;
therefore the power need not be more than half the
weight to make their momentum^ equal.
Caroline. Pulleys act then on the same principle
as the lever, the deficiency of strength of the power
being compensated by its superior velocity.
Mrs. B. You will find, that all mechanical power
is founded on the same principle.
Emily. But may it not be objected to pulleys, that
a longer time is required to raise a weight by their
aid than without it ; for what you gain in power you
lose in time ?
Mrs. B. That, my dear, is the fundamental law
in mechanics : it is the case with the lever, as well
as the pulley ; and you will find it to be so with all
the other mechanical powers.
Caroline. I do not see any advantage in the me-
chanical powers then, if what we gain by them one
way is lost another.
Mrs. B. Since we are not able to increase our
natural strength, is not that science of wonderful
utility, by means of which we may reduce the resist-
ance or weight of any body to the level of our
strength ? This the mechanical powers enable us to
82 ON THE MECHANICAL POWERS.
accomplish, by dividing the resistance of a body into
parts which we can successively overcome. It is
true, as you observe, that it requires a sacrifice of
time to attain this end, but you must be sensible how
very advantageously it is exchanged for power : the
utmost exertion we can make adds but little to our
natural strength, whilst we have a much more un-
limited command of time. You can now understand,
that the greater the number of pulleys connected by
a string the more easily the weight is raised, as the
difficulty is divided amongst the number of strings,
or rather of parts into which the string is divided by
the pulleys. Several pulleys thus connected, form
what is called a system, or tackle of pulleys, (fig. 3.)
You may have seen them suspended from cranes to
raise goods into warehouses, and in ships to draw up
the sails.
Emily. But since a fixed pulley affords us no me-
chanical aid, why is it ever used ?
Mrs. B. Though it does not increase our power,
it is frequently useful for altering its direction. A
single pulley enables us to draw up a curtain by draw-
ing dozvn the string connected with it ; and we should
be much at u loss to accomplish this simple opera-
tion without its assistance.
Caroline. There would certainly be some diffi-
culty in ascending to the head of the curtain, in order
to draw it up. Indeed, I now recollect having seen
workmen raise small weights by this means, which
seemed to answer a very useful purpose.
Mrs. B. In shipping, both the advantages of an
increase of power and a change of direction, by
means of pulleys, are united ; for the sails are raised
up the masts by the sailors on deck, from the change
of direction which the pulley effects, and the labour
is facilitated by the mechanical power of a corbbina-
tion of pulleys.
Emily. But the pulleys on ship-board do not ap-
pear to me to be united in the manner you have
shown us.
ON THE MECHANICAL POWERS. 83
Mrs. B. They are, I believe, generally connect-
ed, as described in figure 4, both for nautical, and a
variety of other purposes ; but in whatever manner
pulleys are connected by a single string, the mecha-
nical power is the same.
The third mechanical power is the wheel and axle.
Let us suppose (plate VI. fig. 5.) tlie weight W to
be a bucket of water in a well, which we raise by
winding the rope, to which it is attached, round the
axle ; if this be done without a wheel to turn the
axle, no mechanical assistance is received. The
axle without a wheel is as impotent as a single fixed
pulley, or a lever, whose fulcrum is in the centre ; but
add the wheel to the axle, and you will immediately
find the bucket is raised with much less difficulty.
The velocity of the circumference of the wheel is as
much greater than that of the axle, as it is further
from the centre of motion ; for the wheel describes
a great circle in the same space of time that the axle
describes a small one ; therefore the power is increas-
ed in the same proportion as the circumference of the
wheel is greater than that of the axle. If the velocity
of the wheel is twelve times greater than that of the
axle, a power nearly twelve times less than the weight
of the bucket would be able to raise it.
Emily. The axle acts the part of the shorter arm
of the lever, the wheel that of the longer arm.
Caroline. In raising water, there is commonly, I
believe, instead of a wheel attached to the axle, on-
ly a crooked handle, which answers the purpose of
winding the rope round the axle, and thus raising
the bucket.
Mrs. B. In this manner (fig. 6.) : now if you ob-
serve the dotted circle which the handle describes
in winding up the rope, you will perceive that the
branch of the handle A, which is united to the axle,
represents the spoke of a wheel, and answers the
purpose of an entire wheel ; the other branch B af-
fords no mechanical aid, merely serving as a handle
to turn the wheel.
^4 ON TlTE MECHANICJAL POWERS.
Wheels are a very essential part of most ma-
chines : they are employed in various ways ; but,
when fixed to the axle, their mechanical power is
always the same ; that is, as the circumference of
the wheel exceeds that of the axle, so much will the
energy of its power be increased.
Caroline. Then the larger the wheel the greater
must be its effect.
Mrs. B. Certainly. If you have ever seen any
considerable mills or manufactures, you must have
admired the immense wheel, the revolution of which
puts the whole of the machinery into motion ; and
though so great an effect is produced by it, a horse
or two has sufficient power to turn it ; sometimes a
stream of water is used for that purpose, but of late
years, a steam-engine has been found both the most
powerful and the most convenient mode of turning
the wheel.
Caroline. Do not the vanes of a windmill repre-
sent a wheel, Mrs. B.
Mrs. B. Yes ; and in this instance we have the
advantage of a gratuitous force, the wind, to turn the
wheel. One of the great benefits resulting from the
use of machinery is, that it gives us a sort of empire
over the powers of nature, and enables us to make
them perform the labour, which would otherwise fall
to the lot of man. When a current of wind, a stream
of water, or the expansive force of steam, performs
our task, we have only to superintend and regulate
their operations.
The fourth mechanical power is the inclined
plane ; this is nothing more than a slope, or declivi-
ty, frequently used to facilitate the drawing up of
weights. It is not difficult to understand, that a
weight may much more easily be drawn up a slope
than it can be raised the same height perpendicu-
larly. But in this, as well as the other mechanical
powers, the facility is purchased by a loss of time
(fig. 7 ) ; for the weight, instead of moving directly
from A to C, must move from B to C, and as the
ON THE MECHANICAL POWERb. 86
length of the plane is to its height, so much is the
resistance of the weight diminished.
Emily. Yes ; for the resistance, instead of being
confined to the short line A C, is spread over the
long line B C.
Mrs. B. The wedge, which is the next mechani-
cal power, is composed of two inclined planes: (fig.
8.) you may have seen wood-cutters use it to cleave
wood. The resistance consists in the cohesive at-
traction of the wood, or any other body which the
wedge is employed to separate ; and the advantage
gained by this power is in the proportion of half its
width to its length ; for while the wedge forces asun-
der the coherent particles of the wood to A and B, it
penetrates downwards as iar as C.
Emily. The wedge, then, is rather a compound
than a distinct mechanical power, since it is compos-
ed of two inclined planes.
Mrs. B. It is so. All cutting instruments are con-
structed upon the principle of the inclined plane, or
the wedge : those that have but one edge sloped, Uke
the chisel, may be referred to the inclined plane :
whilst the axe, the hatchet, and the knife (when used
to split asunder) are used as wedges.
Caroline. But a knife cuts best when it is drawu
across the substance it is to divide. We use it thus
in cutting meat, we do not chop it to pieces.
Mrs. B. The reason of this is, that the edge of a
knife is really a very fine saw, and therefore acts best
when used Uke that instrument.
The screw, which is the last mechanical power, is
more complicated than the others. You will see by
this figure, (fig. 9.) that it is composed of two parts,
the screw and the nut. The screw S is a cylinder,
with a spiral protuberance coiled round it, called
the thread ; the nut N is perforated to contain the
screw, and the inside of the nut has a spiral groove,
made to fit the spiral thread of the screw.
Caroline, It is just like this little box, the lid of
8
86 ON THE MECHANICAL POWERS'.
which screws on the box as you have described ; but
what is this handle which projects from the nut ?
Mrs. B. It is a lever, which is attached to the
nut, without which the screw is never used as a me-
chanical power ; the nut with a lever L attached to
it, is commonly called a winch. The power of the
screw, complicated as it appears, is referable to one
of the most simple of the mechanical powers ;
which of them do yon think it is ?
Caroline. In appearance, it most resembles the
wheel and axle.
Mrs. B. The lever, it is true, has the effect of a
wheel, as it is the means by which you wind the nut
round ; but the lever is not considered as composing
a part of the screw, though it is true, that it is neces-
sarily attached to it. But observe, that the lever,
considered as a wheel, is not fastened to the axle or
screw, but moves round it, and in so doing, the nut
either rises or descends, according to the way in
which you turn it.
Emily. The spiral thread of the screw resembles,
I think, an inclined plane : it is a sort of slope, by
means of wliich the nut ascends more easily than
it would do if raised perpendicularly ; and it serves to
support it when at rest.
Mrs. B. Very well ; if you cut a slip of paper in
the form of an inclined plane, and wind it round your
pencil, which will represent the cylinder, you will find
that it makes a spiral line, corresponding to the spiral
protuberance of the screw. (Fig. 10.)
Emily. Very true ; the nut then ascends an in-
clined plane, but ascends it in a spiral, instead of a
straight line ; the closer the thread of the screw, the
more easy the ascent ; it is like having shallow in-
stead of steep steps to ascend.
Mrs. B. Yes ; excepting that the nut takes no
steps, it gradually winds up or down ; then observe,
that the closer the threads of the screw, the greater
the number of revolutions the winch must make : so
ON THE MECHANICAL POWERS. 87
that we return to the old principle — what is saved in
power is lost in time.
Emily. Cannot the power of the screw be in-
creased also, by lengthening the lever attached to the
nut ?
Mrs. B. Certainly. The screw with the addition
of the lever, forms a very powerful machine, employ-
ed either for compression or to raise heavy weights.
It is used by book-binders, to press the leaves of
books together ; it is used also in cider and wine pres-
ses, in coining, and for a variety of other purposes.
All machines are composed of one or more of
these six mechanical powers we have examined : I
have but one more remark to make to you, relative to
them, which is, that friction in a considerable degree
diminishes their force, allowance must therefore al-
ways be made for it in the construction of machinc-
Caroline. By friction do you mean one part of
the machine rubbing against another part contiguous
to it?
Mrs. B. Yes ; friction is the resistance which
bodies meet with in rubbing against each other ;
there is no such thing as perfect smoothness or even-
ness in nature : polished metals, though they wear
that appearance more than any other bodies, are far
from really possessing it ; and their inequalities may
frequently be perceived through a good magnifying
glass. When, therefore, the surfaces of the two
bodies come into contact, the prominent parts of the
one will often fall into the hollow parts of the other,
and occasion more or less resistance to motion.
Caroline. But if a machine is made of polished
metal, as a watch for instance, the friction must be
very trifling ?
Mrs. B. In proportion as the surfaces of bodies
are well polished, the friction is doubtless diminish-
ed ; but it is always considerable, and it is usually
computed to destroy one third of the power of a ma-
chine. Oil or grease is used to lessen friction :
o8 ON THE MECHANICAL POWERS.
it acts as a polish by filling up the cavities of the rub-
bing surfaces, and thus making them slide more easily
over each other.
Caroline. Is it for this reason that wheels are
greased, and the locks and hinges of doors oiled ?
Mrs. B. Yes ; in these instances the contact of
the rubbing surfaces is so close, and the rubbing so
continual, that notwithstanding their being polished
and oiled, a considerable degree of friction is pro-
duced.
There are two kinds of friction ; the one occasion-
ed by the sliding of the flat surface of a body, the
other by the rolling of a circular body : the friction
resulting from the first is much the most considera-
ble, for great force is required to enable the sliding
body to overcome the resistance which the asperities
of the surfices in contact oppose to its motion, and
it must be either lifted over, or break through them ;
whilst in the other kind of friction, the rough parts
roll over each other with comparative facility ; hence
it is, that wheels are often used for the sole purpose
of diminisliing the resistance of friction.
Emily. This is one of the advantages of carriage-
wheels ; is it not ?
Mrs. B. Yes ; and the larger the circumference
of the wheel the more readily it can overcome any
considerable obstacles, such as stones, or inequalities
in the road. When, in descending a steep hill, we
fasten one of the wheels, we decrease the velocity
of the carriage, by increasing the friction.
Caroline. That is to say, by converting the roll-
ing friction into the dragging friction. And when
you had casters put to the legs of the table, in order
to move it more easily, you changed the dragging in-
to the rolling friction.
Mrs. B. There is another circumstance which
we have already noticed, as diminishing the motiop
of bodies, and which greatly affects the power of
machines. This is the resistance of the medium
in which a machine is worked. All fluids, whether
ON THE MECHANICAL POWERS. 89
of the nature of air or of water, are called me-
diums ; and their resistance is proportioned to their
density ; for the more matter a body contains, the
greater the resistance it will oppose to the motion of
another body striking against it.
Emily. It would then be much more difficult to
work a machine under water than in the air ?
Mrs. B. Certainly, if a machine could be worked
in vacuo, and without friction, it would be perfect ;
but this is unattainable ; a considerable reduction of
power must therefore be allowed for the resistance
of the air.
We shall here conclude our observations on the
mechanical powers. At our next meeting I shall en-
deavour to give you an explanation of the motion of
the heavenly bodies.
S*
CONVERSATION VI.
CAUSES OF THE EARTH'S ANNUAL
MOTION.
Of the Planets, and their Motion — Of the Diurnal Mo'
Hon of the Earth and Planets.
CAROLINE. I am come to you to-day quite
elated with the spirit of opposition, Mrs. B. ; for I
have discovered such a powerful objection to your
theory of attraction, that I doubt whether even your
conjuror Newton, with his magic wand of attraction,
will be able to dispel it.
Mrs. B. Well, my dear, pray what is this weighty
objection ?
Caroline. You say that bodies attract in propor-
tion to the quantity of matter they contain, now we
all know the sun to be much larger than the earth :
why, therefore, does it not attract the earth ; you
will not, I suppose, pretend to say that we are fall-
ing towards the sun ?
Emily. FJowever plausible your objection ap-
pears, Caroline, 1 think you place too much reliance
upon it : when any one has given such convincing
proofs of sagacity and wisdom as Sir Isaac Newton,
when we find that his opinions are universally re-
ceived and adopted, is it to be expected that any ob-
jection we can advance should overturn them ?
Caroline. Yet I confess that I am not inclined to
yield implicit faith even to opinions of the great
Fi^.l.
FLATS VI.
CAUSES, Arc. 91
Newton ; for what purpose are we endowed with
reason, if we are denied the privilege of making use
of it, by judging for ourselves ?
Mrs. B. It is reason itself which teaches us, that
when we, novices in science, start objections to the-
ories established by men of acknowledged wisdom,
we should be diffident rather of our own than of
their opinion. I am far from wishing to lay the least
restraint on your questions; j^ou cannot be better
convinced of the truth of a system, than by finding
that it resists all your attacks, but I would advise
you not to advance your objections with so much con-
fidence, in order that the discovery of their fallacy
may be attended with less mortification. In answer
to that you have just proposed, I can only say, that
the earth really is attracted by the sun.
Caroline. Take care at least that we are not con-
sumed by him, Mrs. B.
Mrs. B. We are in no danger : but our magician
Newton, as you are pleased to call him, cannot
extricate himself from this difficulty without the aid
of some cabilistical figures, which I must draw for
liim.
Let us suppose the earth, at its creation, to have
been projected forwards into universal space ; we
know that if no obstacle impeded its course, it would
proceed in the same direction, and with a uniform
velocity for ever. In fig. 1. plate VI., A represents
the earth, and S the sun. We shall suppose the
earth to be arrived at the point in which it is repre-
sented in the figure, having a velocity which would
carry it on to B in the space of one month ; whilst
the sun's attraction would bring it to C in the same
space of time. Observe that the two fi^rces of pro-
jection and attraction do not act in opposition, but
perpendicularly, or at a right angle to each other.
Can you tell me now, how the earth will move ?
Emily. I recollect your teaching us that a body
acted upon by two forces perpendicular to each other
would move in the diagonal of a parallelogram ; if,
92 CAUSES or the
therefore, I complete the parallelogram by drawing
the lines CD, B D, the earth will move in the dia-
gonal A D.
Mrs. B. A ball struck by two forces acting per-
pendiciilarl}"^ to each other, it is true, moves in the
diagonal of a parallelogram ; but you must observe
that the force of attraction is continually acting upon
our terrestrial ball, and producing an incessant devi-
ation from its course in a right line, which converts
it into that of a curved line ; every point of which
may be considered as constituting the diagonal of an
infinitely small parallelogram.
Let us detain the earth a moment at the point D,
and consider how it will be affected by the combined
action of the two forces in its new situation. It still
retains its tendency to fly off in a straight line ; but
a straight line would now carry it away to F, whilst
the sun would attract it in the direction D S ; how
then will it proceed ?
Emily. It will go on in a curve line in a direction
between that of the two forces.
Mrs. B. In order to know exactly what course the
earth will follow, draw another parallelogram similar
to the first, in which the line D F describes the force
of projection, and the line D S, that of attraction ;
and you will find that the earth will proceed in the
curve line D G.
Caroline. You must now allow me to draw a pa-
rallelogram, Mrs. B. Let me consider in what direc-
tion will the force of projection now impel the earth.
Mrs. B. First draw a line from the earth to the
sun, representing the force of attraction ; then de-
scribe the force of projection at a right angle to it.
Caroline. The earth will then move in the curve
G I, of the parallelogram G li 1 K.
Mrs. B. You recollect that a body acted upon by
two forces, moves through a diagonal in the same
time that it would have moved through one of the
sides of the parallelogram, were it acted upon by one
force only. The earth has passed through the diago-
earth's annual motion. 93
nals of these three parallelograms in the space of
three months, and has performed one quarter of a
circle ; and on the same principle it will go on till it
has completed the whole of the circle. It will then
recommence a course, which it has pursued ever
since it first issued from the hand of its Creator, and
which there is every reason to suppose it will conti-
nue to follow, as long as it remains in existence.
Emily. What a grand and beautiful effect, result-
ing from so simple a cause !
Caroline. It affords an example, on a magnificent
«cale, of the circular motion which you tau2;ht us in
mechanics. The attraction of the sun is the centri-
petal force, which confines the earth to a centre ;
and the impulse of projection the centrifugal force,
which impels the earth to quit the sun and fly off in a
tangent.
Mrs. B. Exactly so. A simple mode of illustra-
ting the effect of these combined forces on the earth,
is to cut a slip of card in the form of a right angle,
(fig. 2. plate VI.) to describe a small circle at the an-
gular point representing the earth, and to fasten the
extremity of one of the legs of the angle to a fixed
point, which we shall consider as the sun. Thus si-
tuated, the angle will represent both the centrifugal
and centripetal forces ; and if you draw it round the
fixed point, you will see how the direction of the cen-
trifugal force varies, constantly forming a tangent to
the circle in which the earth moves, as it is constant-
ly at a right angle with the centripetal force.
Emily. The earth, then, gravitates towards the
sun without the slightest danger either of approach-
ing nearer or receding further from it. How admi-
rably this is contrived! If the two forces which pro-
duce this circular motion had not been so accurately
adjusted, one would ultimately have prevailed over
the other, and we should either have approached so
near the sun as to have been burnt, or have receded
so far from it as to have been frozen.
Mrs. B. What will you say, my dear, when I tell
94 CAUSES OF THE
you, that these two forces are not, in fact, so pro-
portioned as to produce circular motion in the earth?
Caroline. You must explain to us, at least, in what
manner we avoid the threatened destruction.
Mrs. B. Let us suppose that when the earth is at
A, (fig. 3.) its projectile force should not have given
it a velocity sufficient to counterbalance that of gra-
vity, so as to enable these powers conjointly to carry
it round the sun in a circle ; the earth, instead of de-
scribing the line A C, as in the former figure, vvill
approach nearer the sun in the line A B.
Caroline. Under these circumstances, I see not
what is to prevent our approaching nearer and nearer
the sun till we fall into it ; for its attraction increases
as we advance towards it, and produces an accelerated
velocity in the earth, which increases the danger.
Mrs. B. And there is yet another danger, of
which you are not aware. Observe, that as the
earth approaches the sun, the direction of its projec-
tile force is no longer perpendicular to that of attrac-
tion, but inclines more nearly to it. When the earth
reaches that part of its orbit at B, the force of projec-
tion would carry it to D, which brings it nearer the
sun instead of bearing it away from it.
Emily. If, then, we are driven by one power and
drawn by the other to this centre of destruction, how
is it possible for us to escape ?
Mrs. B. A little patience, and you will find that
we are not without resource. The earth continues
approaching the sun with a uniformly increasing ac-
celerated motion, till it reaches the point E ; in what
direction will the projectile force now impel it?
Emily. In the direction E F. Here then the two
forces act perpendicularly to each other, and the
earth is situated just as it was in the preceding figure ;
therefore, from this point, it should revolve round the
sun in a circle.
Mrs. B. No, all the circumstances do not agree.
In motion round a centre, you recollect that the cen-
trifugal force increases with the velocity of the body.
earth's annual motion. 95
or, in other words, the quicker it moves the stronger
is its tendency to fly ofl' in a right line. When the
earth, therefore, arrives at E, its accelerated motion
will have so far increased its velocity, and consequent-
ly its .centrifugal force, that the latter will prevail over
the force of attraction, and drag the earth away from
the sun till it reaches G.
Caroline. It is thus, then, that we escape from
the dangerous vicinity of the sun ; and in proportion
as we recede from it, the force of its attraction, and,
consequently, the velocity of the earth's motion, are
diminished.
Mrs. B. Yes. From G the direction of projection
is towards H, that of attraction towards S, and the
earth proceeds between them with a uniformly re-
tarded motion, till it has completed its revolution.
Thus you see, that the earth travels round the sun,
not in a circle, but an ellipsis, of which the sun
occupies one of the foci; and that in its course the
earth alternately approaches and recedes from it,
without any danger of being either swallowed up, or
of being entirely carried away from it.
Caroline. And 1 observe, that what I apprehended
to be a dangerous irregularity, is the means by which
the most perfect order and harmony are produced !
Emily. The earth travels, then, at a very unequal
rate, its velocity being accelerated as it approaches
the sun, and retarded as it recedes from it.
Mrs. B. It is mathematically demonstrable, that,
in moving round a point towards which it is attracted,
a body passes over equal areas in equal times. The
whole of the space contained within the earth's orbit,
is, in fig. 4, divided into a number of areas, or spaces,
1, 2, 3, 4, &.C. all of which are of equal dimensions,
though of very different forms ; some of them, you
see, are long and narrow, others broad and short ; but
they each of them contain an equal quantity of space.
An imaginary line drawn from the centre of the earth
to that of the sun, and keeping pace with the earth
in its revolution, passes over equal areas in equal
96 CAUSES OF THE
times ; that is to say, if it is a month going from A to
B, it will be a month going from B to C, and another
from C to E, and so on.
Caroline. What long journeys the earth has to
perform in the course of a month, in one part of her
orbit, and how short they are in the other part!
Mrs. B. The inequality is not so considerable as
appears in this figure ; for the earth's orbit is not so
eccentric as it is there described ; and, in reality,
differs but little from a circle : that part of the earth's
orbit nearest the sun is called its perihelion, that part
most distant from the sun its aphelion; and the earth
is above three millions of miles nearer the sun at its
perihelion than at its aphelion.
Emily. I think I can trace a consequence from
these different situations of the earth ; is it not the
cause of summer and winter?
Mrs. B. On the contrary ; during the height of
summer, the earth is in that part of its orbit which is
most distant from the sun, and it is during the severity
of winter that it approaches nearest to it.
Emily. That is very extraordinary; and how then
do you account for the heat being greatest when we
are most distant from the sun ?
Mrs. B. The difference of the earth's distance
from the sun in summer and winter, when compared
with its total distance from the sun, is but inconsidera-
ble. The earth, it is true, is above three millions of
miles nearer the sun in winter than in summer ; but
that distance, however great it at first appears, sinks
into insignificance in comparison of 95 millions of
miles, which is our mean distance from the sun. The
change of temperature, arising from this difference,
would scarcely be sensible ; were it not completely
overpowered by other causes which produce the va-
riations of the seasons ; but these I shall defer explain-
ing, till we have made some further observations on
the heavenly bodies.
Caroline. And should not the sun appear smaller
in summer, when it is so much further from us ?
earth's annual motion. 97
Mrs. B. It actually does, when accurately mea-
sured ; but the apparent difference in size is, I be-
lieve, not perceptible to the naked eye.
Emily. Then, since the earth moves with greatest
velocity in that part of its orbit nearest the sun, it
must have completed its journey through one half of
its orbit in a shorter time than the other half?
Mrs. B. Yes, it is about seven days longer per-
forming the summer half of its orbit than the winter
half.
The revolution of all the planets round the sun is
the result of the same causes, and is performed in
the same manner as that of the earth.
Caroline. Pray what are the planets ?
Mrs. B. They are those celestial bodies, which
-revolve like our earth about the sun ; they are sup-
posed to resemble the earth also in many other re-
spects ; and we are led by analogy to suppose them
to be inhabited worlds.
Caroline. I have heard so ; but do you not think
such an opinion too great u stretch of the imagina-
tion ?
Mrs. B. Some of the planets are proved to be
larger than the earth ; it is only their immense dis-
tance from us, which renders their apparent dimen-
sions so small. Now, if we consider them as enor-
mous globes, instead of small twinkling spots, we
shall be led to suppose, that the Almighty would not
have created them merely for the purpose of giving
us a little light in the night, as it was formerly ima-
gined, and we should find it more consistent with
our ideas of the Divine wisdom and beneficence, to
suppose that these celestial bodies should be created
for the habitation of beings, who are, like us, bless-
ed by His providence. Both in a moral as well as
a physical point of view, it appears to me more ra-
tional to consider the planets as worlds revolving
round the sun ; and the fixed stars as other suns,
each of them attended by their respective system of
planets, to which they impart theif influence ? We
9
98 CAUSES OF THE
have brought our telescopes to such a degree of per-
fection, that from the appearances which the moon
exhibits when seen through them, we have very good
reason to conclude, that it is a habitable globe, for
though it is true, that we cannot discern its towns
and people, we can plainly perceive its mountains
and valleys ; and some astronomers have gone so far
as to imagine they discovered volcanos.
Emily. If the fixed stars are suns, with planets
revolving round them, why should we not see those
planets as well as their suns ?
Mrs. B. In the first place, we conclude that the
planets of other systems, (like those of our own,) are
much smaller than the suns which give them light ;
therefore at so great a distance as to make the suns
appear like fixed stars, the planets would be quite
invisible. Secondly, the light of the planets being
only reflected light, is much more feeble than that of
the fixed stars. There is exactly the same difference
as between the light of the sun and that of the moon;
the first being a fixed star, the second a planet.
Emily. But if the planets are worlds like our
earth, they are dark bodies ; and instead of shining
by night, we should see them only by daylight. —
And why do we not see the fixed stars also by day-
light?"
Mrs. B. Both for the same reason ; — their light
is so faint, compared to that of our sun reflected by
the atmosphere, that it is entirely eff'aced by it : the
light emitted by the fixed stars may probably be as
strong as that of our sun, at an equal distance ; but
being so much more remote, it is difl'used over a
greater space, and is consequently proportionally
■weakened.
Caroline. True ; I can see much better by the
light of a candle that is near me, than by that of one
at a great distance. But I do not understand what
makes the planets shine ?
Mrs. B. What is it that makes the steel buttons
on your brother's coat shine ?
earth's annual M0TI0I7. 99
Caroline. The sun. But if it was the sun which
made the planets shine, we should see them in the
day-time, when the sun shone upon them ; or if the
fjiintness of their light prevented our seeing them in
the day, we should not see them at all, for the sun
cannot shine upon them in the night.
Mrs. B. There you are in error. But in order to
explain this to you, I must first make you acquainted
with the various motions of the planets.
You know, that according to the laws of attraction,
the planets belonging to our system all gravitate to-
wards the sun : and that this force combined with
that of projection, will occasion their revolution
round the sun, in orbits more or less elliptical, ac-
cording to the proportion which these two forces
bear to each other.
But the planets have also another motion : they
revolve upon their axes. The axis of a planet is an
imaginary line which passes through its centre, and
on which it turns ; and it is this motion which pro-
duces day and night. With that side of the planet
facing the sun, it is day ; and with the opposite side,
which remains in darkness, it is night. Our earth,
which we consider as a planet, is 24 hours in per-
forming one revolution on its axis : in that period of
time, therefore, we have a day and a niglit ; hence
this revolution is called the earth's diurnal or daily
motion ; and it is this revolution of the earth from
west to east which produces an apparent motion of
the sun, moon and stars in a contrary direction.
Let us now suppose ourselves to be beings, inde-
pendent of any planet, travelling in the skies, and
looking upon the earth in the same point of view as
upon the other planets.
Caroline. It is not flattering to us, its inhabitants,
to see it make so insignificant an appearance.
Mrs. B. To those who are accustomed to contem-
plate it in this light, it never appears more glorious.
We are taught by science to distrust appearances ;
and instead of considering the planets as little stars,
100 CAUSES OF THE
we look np6n them either as hrilliant suns or habitable
worlds, and we consider the whole together as form-
ing one vast and magnificent system, worthy of the
Divine hand b}' which it was created.
Emily. I can scarcely conceive the idea of this
immensity of creation ;Mt seems too sublime for our
imagination : — and to think that the goodness of Pro-
vidence extends over millions of worlds throughout a
boundless universe — Ah ! Mrs. B., it is we only who
become trifling and insignificant beings in so magni-
iScent a creation !
Mrs. B. This idea should teach us humility, but
without producing despondency. The same Almighty
})and which guides these countless worlds in their un-
deviating course, conducts with equal perfection the
])lood as it circulates through the veins of a fly, and
opens the eye of the insect to behold His wonders.
Notwithstanding this immense scale of creation,
therefore, we need not fear to be disregarded or for-
gotten.
But to return to our station in the skies. We
were, if you recollect, viewing the earth at a great
distance, in appearance a little star, one side illumin-
ed by the sun, the other in obscurity. But would you
believe it, Caroline, many of the inhabitants of this little
star imagine that when that part which they inhabit
is turned from the sun, darkness prevails throughout
the universe, merely because it is night with them ;
whilst, in reality, the sun never ceases to shine upon
every planet. When, therefore, these little igno-
rant beings look around them during their night,
and behold all the stars shining, they cannot ima-
gine why the planets, which are dark bodies, should
shine, concluding, that since the sun docs not illu-
mine themselves, the whole universe must be in
darkness.
Caroline, I confess that I was one of these igno-
rant people ; but I am now very sensible of the ab-
surdity of such an idea. To the inhabitants of the other
planets, then, we must appear as a little star ?
earth's annual motion. 101
Mrs. B. Yes, to those which rerolve round our
sun ; for since those which may belong to other
systems, (and whose existence is only hypothetical,)
are invisible to us, it is probable, that we also are
invisible to them.
Emily. But they may see our sun as we do theirs,
ip appearance a fixed star ?
Mrs. B. No doubt ; if the beings who inhabit
those planets are endowed with senses similar to ours.
By the same rule, we must appear as a moon to the
inhabitants of our moon ; but on a larger scale, as
the surface of the earth is about thirteen times as
large as that of the moon.
Emily. The moon, Mrs. B., appears to move in
a different direction, and in a different manner from
the stars ?
Mrs. B. I shall defer the explanation of the mo-
tion of the moon, till our next interview, as it would
prolong our present lesson too much.
9*
CONVERSATION VIL
ON THE PLANETS.
Of the Satellites or Moons. — Gravity diminishes as the
Square of the Distance. — Of the Solar System. — Of
Comets — Constellations, Signs of the Zodiac. — Of
Copernicus, Newton, 4'C.
MRS. B. The planets are distinguished into pri-
mary and secondary. Those which revolve immedi-
ately about the sun are called primary. Many of these
are attended in their course by smaller planets, which
revolve around them : these are called secondary
planets, satellites, or moons. Such is our moon,
which accompanies the earth, and is carried with it
round the sun.
Emily. How then can you reconcile the motion
of the secondary planets to the laws of gravitation ;
for the sun is much larger than any of the primary
planets ; and is not the power of gravity proportion-
al to the quantity of matter ?
Caroline. Perhaps the sun, though much larger,
may be less dense than the planets. Fire you know
is very light, and it may contain but little matter,
though of great magnitude.
Mrs. B. We do not knOw of what kind of matter
the sun is made ; but we may be certain, that since
it is the general centre of attraction of our system of
planets, it must be the body which contains the great-
est quantity of matter in that system.
Yoa must recollect, that the force of attraction i*
ON THE PLANETS. 10^
not only proportional to the quantity of matter, but to
the degree of proximity of the attractive body : this
power is weakened by being diflfused, and diminishes
as the squares of the distances increase. The square
is the product of a number multiplied by itself; so
that a planet situated at twice the distance at which
we are from the sun would gravitate four times less
than we do ; for the product of two multiplied by it-
self is four.
Caroline. Then the more distant planets move
slower in their orbits ; for their projectile force must
be proportioned to that of attraction ? But I do not
see how this accounts for the motion of the secondary
round the primary planets, in preference to the sun ?
Emily. Is it not because the vicinity of the pri-
mary planets renders their attraction stronger than
that of the sun ?
Mrs. B. Exactly so. But since the attraction be-
tween bodies is mutual, the primary planets are also
attracted by the satellites, which revolve round them.
The moon attracts the earth, as well as the earth the
moon ; but as the latter is the smaller body, her at-
traction is proportionally less ; therefore neither the
earth revolves round the moon, nor the moon round
the earth ; but they both revolve round a point,
which is their common centre of gravity, and which
is as much nearer the earth than the moon, as the gra-
vity of the former exceeds that of the latter.
Emily. Yes, I recollect your saying, that if two
bodies were fastened together by a wire or bar, their
common centre of gravity would be in the middle of
the bar, provided the bodies were of equal weight ;
and if they differed in weight, it would be nearer the
larger body. If then the earth and moon had no pro-
jectile force which prevented their mutual attraction
from bringing them together, they would meet at their
common centre of gravity.
Caroline. The earth then has a great variety of
motions : it revolves round the sun, upon its axis, and
round the point towards which the moon attracts it.
104 ON THE PLANETS.
Mrs. B. Just so; and this is the case with every
planet which is attended by satelhtes. The compli-
cated effect of this variety of motions, produces cer-
tain irregularities, which, however, it is not necessa-
ry to notice at present.
The planets act on the sun in the same manner as
they are themselves acted on by their satellites ; for
attraction, you must remember, is always mutual ; but
the gravity 0/ the planets (even when taken collec-
tively) is so trifling compared with that of the sun,
that they do not cause the latter to move so much as
one half of his diameter. The planets do not, there-
fore, revolve round the centre of the sun, but round
a point at a small distance from its centre, about
which the sun also revolves.
Emily. I thought the sun had no motion?
Mrs. B. You were mistaken ; for, besides that
which I have just mentioned, which is indeed very
inconsiderable, he revolves on his axis ; this motion
is ascertained by observing certain spots which disap-
pear, and re-appear regularly at stated times.
Caroline. A planet has frequently been pointed
out to me in the heavens ; but I could not perceive
that its motion differed from that of the fixed stars,
which only appear to move.
Mrs. B. The great distance of the planets renders
their motion apparently so slow, that the eye is not
sensible of their progress in their orbit, unless we
watch them for some considerable length of time : in
different seasons they appear in different parts of the
heavens. The most accurate idea 1 can give you of
the situation and motion of the planets, will be by the
examination of this diagram, (Plate VII. fig. 1.) repre-
senting the solar system, in which you will find every
planet with its orbit delineated.
Emily. But the orbits here are all circular, and
you said that they were elliptical. The planets ap-
pear, too, to be moving round the centre of the sun ;
whilst you told us, that they moved round a point at
a little distance from thence.
PLATE Vn.
Fi^.
Ft^. 2.
Mars yemis Forth
^'-y "o o o
Moon
Hertchel
n
t)N THE PLACETS. 105
Mrs. B. The orbits of the planets nre so nearly
circular, and the common centre of gravity of the so-
lar system so near the centre of the sun, that these
deviations are scarcely worth observing. The di-
mensions of the planets, in their true proportions,
you will find delineated in fig. 2.
Mercury is the planet nearest the sun ; his orbit is
consequently contained within ours ; but his vicinity
to the sun, occasions his being nearly lost in the bril-
liancy of his rays ; and when we see the sun, he is so
dazzling, that very accurate observations cannot be
made upon Mercury. He performs his revolution
round the sun in about 87 days, which is consequent-
ly the length of his year. The time of his ro-
tation on his axis is not known ; his distance from the
sun is computed to be 37 millions of miles, and his
diameter 3180 miles. The heat of this planet is so
great, that water cannot exist there, but in a state of
vapour, and metals would be liquified.
Caroli7ie. Oh, what a dreadful climate!
Mrs. B. Though we could not live there, it may
be perfectly adapted to other beings destined to inha-
bit it.
Venus, the next in the order of planets, is 68 mil-
lions of miles from the sun : she revolves about her
axis in 23 hours and 21 minutes, and goes round the
sun in 244 days 17 hours. The orbit of Venus is also
within ours ; during one half of her course in it, we
see her before sunrise, and she is called the morning
star ; in the other part of her orbit, she rises later
than the sun.
Caroline. In that case, we cannot see her, for she
must rise in the day time ?
Mrs. B. True ; but when she rises later than the
sun, she also sets later ; so that we perceive her ap-
proaching the horizon after sunset : she is then call-
ed Hesperus, or the evening star. Do you recollect
those beautiful lines of Milton :
Now came still evening on, and twilight grav
Had in her sober livery all things clad;.
f
106 ON THE PLANETS.
Silence accompanied ; for beast and bird,
They to their grassy couch, these to their nests
Were slunk, all but the wakeful nightingale ;
She all night long her amorous descant sung;
Silence was pleas'd : now glowed the firmament
With living saphirs: Hesperus, that led
The starry host, rode brightest, till the m6on
Rising in clouded majesty, at length
Apparent queen unveil'd her peerless light,
And o'er the dark her silver mantle threw.
The planet next to Venus is the Earth, of which
we shall soon speak at full length. At present I shall
only observe that we are 95 millions of miles distant
from the sun, that we perform our annual revolution
in 365 days 5 hours and 49 minutes ; and are attend-
ed in our course by a single moon.
Next follows Mars. He can never come between
us and the sun, like I\rercury and Venus ; his motion
is, however, very perceptible, as he may be traced
to different situations in the heavens ; his distance
from the sun is 144 millions of miles ; he turns
rounds his axis in 24 hours and 39 minutes ; and he
performs his annual revolution, in about 687 of our
days : his diameter is 4120 miles.. Then follow four
very small planets, Juno, Ceres, Pallas, and Vesta,
which have been recently discovered, but whose di-
mensions and distances from the sun have not been
very accurately ascertained.
Jupiter is next in order : this is the largest of all
the planets. He is about 490 millions of miles from
the sun, and completes his annual period in nearly
twelve of our years. He turns round his axis in
about ten hours. He is above 1200 times as big as
our earth ; his diameter being 86,000 miles. The
respective proportions of the planets cannot, there-
fore, you see, be conveniently delineated in a dia-
gram. He is attended by four moons.
The next planet is Saturn, whose distance from the
sun is about 900 millions of miles ; his diurnal rota-
tion is performed in 10 hours and a quarter : — his an-
nual revolution in nearly 30 of our years. His dia-
ON THE PLANETS. 107
meter is 79,000 miles. This planet is surrounded
hy a luminous ring, the nature of which, astronomers
are much at a loss to conjecture ; he has seven
moons. Lastly, we observe the Georgium Sidus, disco-
vered by Dr. Herschel, and which is attended by six
moons.
Caroline. How charming; it must be in the distant
planets, to see several moons shining at the eame
time ; I think I should like to be an inhabitant of Ju-
piter or Saturn.
Mrs. B. Not long, I believe. Consider what ex-
treme cold must prevail in a planet, situated as Saturn
is, at nearly ten times the distance at which we are from
the sun. Then his numerous moons are far from
making so splendid an appearance as ours ; for they
can reflect only the light which they receive from the
sun ; and both light and heat decrease in the same
ratio or proportion to the distances as gravity. Caa
you tell me now how much more light we enjoy
than Saturn ?
Caroline. The square of ten is a hundred ; there-
fore, Saturn has a hundred times less — or to answer
your question exactly, we have a hundred times
more light and heat than Saturn — this certainly does
not increase my wish to become one of tbe poor
wretches who inhabit that planet.
Mrs. B. May not the inhabitants of Mercury,
with equal plausibility, pity us, for the insupportable
coldness of our situation ; and those of Jupiter and
Saturn for our intolerable heat ? The x'Mmighty Pow-
er which created these planets, and placed them in
their several orbits, has no doubt peopled them with
beings whose bodies are adapted to the various tem-
peratures and elements in which they are situated.
If we judge from the analogy of our own earth, or
from that of the great and universal beneficence of
Providence, we must conclude this to be the case.
Caroline. Are not comets also supposed to be
planets ?
Mrs. B. Yes, they are ; for by the re-appear-
108 ON THE PLANETS.
ance of some of them, at stated times, they are
known to revolve round the sun, but in orbits so ex-
tremely eccentric, that they disappear for a great
number of years. If they are inhabited, it must be
by a species of beings very different, not only from
the inhabitants of this, but from those of any of the
other planets, as they must experience the greatest
vicissitudes of heat and cold ; one part of their orbit
being so near the sun, that their heat, when there,
is computed to be greater than that of red-hot iron ;
in this part of its orbit, the comet emits a luminous
vapour, called the tail, which it gradually loses as it
recedes from the sun ; and the comet itself totally
disappears from our sight, in the more distant parts
of its orbit, which extends considerably beyond that
of the furthest planet.
The number of comets belonging to our system
cannot be ascertained, as some of them are whole
centuries before they make their re-appearance.
The number that are known by their regular re-ap-
pearance is only three.
Emily. Pray, Mrs. B., what are the constellations?
Mrs. B. They are the fixed stars, which the an-
cients, in order to recognise them, formed into
groups, and gave the names of the figures which you
find delineated on the celestial globe. In order to
show their proper situations in the heavens, they
should be painted on the internal surface of a hollow
sphere, from the centre of which you should view
them ; you would then behold them, as they appear
to be situated in the heavens. The twelve constel-
lations, called the signs of the zodiac, are those which
are so situated, that the earth in its annual revolution
passes directly between them and the sun. Their
names are Aries, Taurus, Gemini, Cancer, Leo, Vir-
go, Libra, Scorpio, Sagittarius, Capricornus, Aquari-
us, Pisces ; the whole occupj'ing a complete circle,
or broad belt, in the heavens, called the zodiac.
(Plate VIIl. fig. 1.) Hence a right line drawn from
the earth, and passing through the sun, would reach
TLATE vm.
ON THE PLANETS. 109
one of these constellations, and the sun is said to be
in that constellation at which the line terminates: thus,
when the earth is at A, the sun would appear to be
in the constellation or sign Aries ; when the earth is
at B, the sun would appear in Cancer ; when the
earth was at C, the sun would be in Libra ; and when
the earth was at D, the sun would be in Capricorn.
This circle, in which the sun thus appears to move,
and which passes through the middle of the zodiac,
is called the ecliptic.
Caroline. But many of the stars in these constel-
lations appear beyond the zodiac.
Mrs. B. We have no means of ascertaining the
distance of the fixed stars. When, therefore, they
are said to be in the zodiac, it is merely implied, that
they are situated in that direction, and that they shine
upon us through that portion of the heavens which
we call the zodiac.
Emily. But are not those large bright stars, which
are called stars of the first magnitude, nearei* to us
than those small ones which we can scarcely discern?
Mrs. B. It may be so ; or the difference of hze
and brilliancy of the stars may proceed from their
difference of dimensions ; this is a point which as-
tronomers are not enabled to determine. Consider-
ing them as suns, I see no reason why different suns
should not vary in dimensions, as well as the planets
belonging to them.
Emily. What a wonderful and beautiful system this is,
and how astonishing to think that every fixed star ma/
probably be attended by a similar train of planets I
Caroline. You will accuse me of being very in-
credulous, but I cannot help still entertaining some
doubts, and fearing that there is more beauty than
truth in this system. It certainly may be so ; but
there does not appear to me to be sufficient evidence
to prove it. It seems so plain and obvious that the
earth is motionless, and that the sun and stars revolve
round it ; — your solar system, you must allow, is di-
rectly in opposition to the evidence of our senses.
10
110 ON THE PLANETS.
Mrs. J5. Our senses so often mislead us, that we
should not place implicit reliance upon them.
Caroline. On what then can we rely, for do we
not receive all our ideas through the medium of our
senses ?
Mrs. B. It is true, that they are our primary
source of knowledge ; but the mind has the power
of reflecting, judging, and deciding upon the ideas
received by the organs of sense. This faculty, which
we call reason, has frequently proved to us, that our
senses are liable to err. If you have ever sailed on
the water, with a very steady breeze, you must have
seen the houses, trees and every object move while
you were sailing.
Caroline. I remember thinking so, when I was
very young : but I now know that their motion is
only apparent. It is true that my reason, in this case,
corrects the error of my sight.
Mrs. B. It teaclies you, that the apparent motion
of the objects on shore, proceeds from your being
yourself moving, and that you are not sensible of
yqpr own motion, because you meet with no resist-
ance. It is only when some obstacle impedes our
motion, that we are conscious of moving; and if you
were to close your eyes when you were sailing on
calm water, with a steady wind, you woujd not per-
ceive that you moved, for you could not feel it, and
you could see it only by observing the change of
place of the objects on shore. So it is with the mo-
tion of the earth ; every thing on its surface, and the
air that surrounds it, accompanies it in its revolution ;
it meets with no resistance ; therefore, like the crew
of a vessel sailing with a fair wind, in a calm sea, we
arc insensible of our motion.
Caroline. But the principal reason why the crew
of a vessel in a calm sea do not perceive the motion,
is, because they move exceedingly slowly ; while the
earth, you say, revolves with great velocit3^
Mrs^ B. It is not because they move slowly, but
because they move steadily, and meet with no ir-
ON THE I'LAXETS. HI
regular resistances, that the crew of a vessel do no!
perceive their motion ; for they would be equally
insensible to it, with the strongest wind, provided it
were steady, that they sailed with it, and that it did
not agitate the water ; but this last condition, you
know, is not possible, for the wind will always pro-
duce waves, which offer more or less resistance to
the vessel, and then the motion becomes sensible
because it is unequal.
Caroline. But, granting this, the crew of a vessel
have a proof of their motion, though insensible,
which the inhabitants of the earth cannot have — the
apparent motion of the objects on shore.
Mrs. B. Have we not a similar proof of the earth's
motion, in the apparent motion of the sun and stars.
Imagine the earth to be sailing round its axis, and
successively passing by every star, which, like the
objects on land, we suppose to be moving instead
of ourselves. 1 have heard it observed by an aerial
traveller in a balloon, that the earth appears, to sink
beneath the balloon, instead of the balloon rising
above the earth.
It is a law which we discover throughout nature, and
worthy of its great Author, that all its purposes are
accomplished by the most simple means ; and what
reason have we to suppose this law infringed, in or-
der that we may remain at rest, while the sun and
stars move round us ; their regular motions, which
are explained by the laws of attraction on the first
supposition, would be unintelligible on the last, and
the order and harmony of the universe be destroyed.
Think what an immense circuit the sun and stars
would make daily, were their apparent motions real.
We know many of them to be bodies more consider-
able than our earth ; for our eyes vainly endeavour
to persuade us, that they are little brilliants spark-
ling in the heavens, while science teaches us that
they are immense spheres, whose apparent dimen-
sions are diminished by distance. Why then should
these enormous globes daily traverse -such a prodi-
112 ON THE PLANETS.
gions space, merely to prevent the necessity of our
earth's revolving on its axis ?
Caroline. I think I must now be convinced. But
3'ou vpill, I hope, allow me a little time to familiarize
m^'^self to an idea so diirerent from that which 1 have
been accustomed to entertain. And pray, at what
rate do we move ?
Mrs. B. The motion produced by the revolution
of the earth on its axis, is about eleven miles a mi-
nute, to an inhabitant of London.
Emily. But docs not every part of the earth move
with the same velocity ?
Mrs. B. A moment's reflection would convince
you of the contrary ; a person at the equator must
move quicker than one situated near the poles, since
they both perform a revolution in 24 hours.
Emily. True, the equator is farthest from the axis
of motion. But in the earth's revolution round the
sun, every part must move with equal velocity ?
Mrs. B. Yes, about a thousand miles a minute.
Caroline. How astonishing! — and that it should
be possible for us to be insensible of such a rapid mo-
tion. You would not tell me this sooner, Mrs. B., for
fear of increasing my incredulity.
Before the time of Newton, was not the earth sup-
posed to be in the centre of the system, and the sun,
moon, and stars to revolve round it ?
Mrs. B. This was the system of Ptolemy in an-
cient times ; but as long ago as the beginning of the
sixteenth century it was discarded, and the solar sys-
tem, such as I have shown you, was established by
the celebrated astronomer Copernicus, and is hence
called the Copernican system. But the theory of
gravitation, the source from which this beautiful and
harmonious arrangement flows, we owe to the pow-
erful genius of Newton, who lived at a much later
period.
Emily. It appears, indeed, fiir less diflicult to trace
by observation the motion of the planets, than to di-
vine by what power they are impelled and guided. I
ON THE PLANETS. 113
wonder how the idea of gravitation could first have
occurred to Sir Isaac Newton ?
Mrs. B. It is said to have been occasioned by a
circumstance from which one should little have ex-
pected so grand a theory to have arisen. During
the prevalence of the plague in the year 1665, New-
ton retired into the country to avoid the contagion :
when sitting one day in his orchard, he observed
an apple fall from a tree, and was led to consider
what could be the cause which brought it to the
ground.
Caroline. If I dared to confess it, Mrs. B., I should
say that such an inquiry indicated rather a deficiency
than a superiority of intellect. I do not understand
how any one can wonder at what is so natural and so
common.
Mrs. B. It is the mark of superior genius to find
matter for wonder, observation, and research, in cir-
cumstances which, to the ordinary mind, appear tri-
vial, because they are common, and with which they
are satisfied, because they are natural, without re-
flecting that nature is our grand field of observation,
that within it is contained our whole store of know-
ledge ; in a word, that to study the works of nature,
is to learn to appreciate and admire the wisdom of
God. Thus, it was the simple circumstance of the
fall of an apple, which led to the discovery of the
laws upon whigh the Copernican system is founded ;
and whatever credit this system had obtained before,
it now rests upon a basis from which, it cannot be
shaken.
Emily. This was a most fortunate apple, and more
worthy to be commemorated than all those that have
been sung by the poets. The apple of discord for
which the goddesses contended ; the golden apples by
which Atalanta won the race; nay, even the applQ
which William Tell shot from the head of his son
cannot be compared to this !
10*
CONVERSATION Vllf.
ON THE EARTH.
Of the Terrestrial Globe.— Of the Figure of the Earth,
— Of the Pendulum. — Of the Variation of the Sea-
sons, and of the Length of Days and JVights. — Of
the causes of the Heat of Summer. — Of Solar, Side-
rial, and Equal or Mean Time,
MRS. B. As the earth is the planet in wliich we
are the most particuhirly interested, it is my intention.
this mornina;, to explain to you the effects resulting
li'om its annual and diurnal njotions ; but for this pur-
pose it will bo necessary to make you acquainted with
the terrestrial globe : you have not either of you, I
conclude, learnt the use of the g;h:)bes ?
Carnline. No ; I once indeed loarnt by heart the
names of the lines marked on the globe, but as 1 was
informed they were only imaginary divisions, they
did not appear to me worthy of much attention, and
were soon fori^otten.
Mrs. B. You supposed, then, that astronomers
had been at the trouble of inventing a number uf lines
to little purpose. It will be impossible for me to ex-
plain to you the particular effects of the earth's mo-
tion, without your having acquired a knowledge of
these lines : in Plate Vlll. fig. 2. you will find them
ail delineated : and you mu'^t learn them perfectly if
you wish to make any proficiency in astronomy.
Caroline. I was taught them at so early an age
that I could not understand their meaning ; and I
have often heard you say that the only use of words
was to convey ideas.
ON THE EARTH. lib
Mrs. B. The names of these lines would have
conveyed ideas of the tigures they were designed to
express, though the use of these tigures might at that
time have been too difficult for you to understand.
Childhood is the season when impression*^ on the me-
mory are most strongly and most easily made : it is
the period at which a large stock of ideas should be
treasured up, the application of which we may learn
when the understanding is more developed. It is, I
think, a very mistaken notion that children should be
taught such things only as they can perfectly under-
stand. Had you been early made acquainted with the
terms which relate to figure and motion, how much it
would have facilitated your progress in natural philo-
sophy. I have been obliged to confine myself to the
most common and familiar expressions, in explaining
the laws of nature, though I am convinced that ap-
propriate and scientific terms would have conveyed
more precise and accurate ideas ; but 1 was afraid of
not being understood.
Emily. You may depend upon our learning the
names of these lines thoroughly, Mrs. B. ; but, before
we commit them to memory, will you have the good-
ness to explain them to us ?
Mrs. B. Most willingly. This globe, or sphere,
represents the earth ; the line which passes through
its centre, and on which it turns, is called its axis :
and the two extremities of the axis, A and B, are the
poles, distinguished by the names of the north and the
south pole. The circle C D, which divides the globe
into two equal parts between the poles, is called the
equator, or equinoctial line ; that part of the globe to
the north of the equator is the northern hemisphere ;
that part to the south of the equator, the southern
Iiemisphere. The small circle E F, which surrounds
the north pole, is called the arctic circle ; that G H,
which surrounds the south pole, the antarctic circle.
There are two intermediate circles between, the
polar circles and the equator; that to the north,
I K, called the tropic of Cancer ; that to the souths
110 OJJ THE EARTfir.
L M, called the tropic of Capricorn. Lastly, thi
circle, L K, which divides the globe into two equal
parts, crossing the equator and extending northward
as far as the tropic of Cancer, and southward as
far as the tropic of Capricorn, is called the ecliptic.
The delineation of the ecliptic on the terrestrial
globe is not without danger of conveying false ideas ;
for the ecliptic (as I have before said) is an imagi-
nary circle in the heavens passing through the mid-
dle of the zodiac, and situated in the plane of the
earth's orbit.
Caroline. I do not understand the meaning of the
plane of the earth's orbit.
Mrs. D. A plane, or plain, is an even level sur-
face. Let us suppose a smooth thin solid plain cut-
ting the sun through the centre, extending out as far
as the tixed stars, and terminating in a circle which
passes through the middle of the zodiac ; in this plane
the earth would move in its revolution round the sun ;
it is therefore called the plane of the earth's orbit,
and the circle in which this plane cuts the signs of
the zodiac is the ecliptic. Let the fig. 1. Plate IX.
represent such a plane, S the sun, E the earth with
its orbit, and A B C D the ecliptic passing through the
middle of the zodiac.
Emily. If the ecliptic relates only to the heavens,
why is it described upon the terrestrial globe ?
Mrs. B. It is convenient for the demonstration of
a variety of problems in the use of the globes ; and
besides, the obliquity of this circle to the equator is
rendered more conspicuous by its being described on
the same globe ; and the obliquity of the ecliptic
shows the inclination of the earth's axis to the plane
of its orbit. But to return to fig. 2. Plate VIH.
The spaces between the several parallel circles on
the terrestrial globe are called zones ; that which is
comprehended between the tropics is distinguished by
the name of the torrid zone ; the spaces which ex-
tend from the tropics to the polar circles, the north
ON THE EARTH. 117
and south temperate zones ; and the spaces contain-
ed within the polar circles, the frigid zones. .
The several lines which, you observe, are drawn
from one pole to ihe other, cutting the equator at
right angles, are called meridians. When any one of
these meridians is exactly opposite the sun it is mid-
day, or twelve o'clock in the day, with all the places
situated on that meridian ; and, with the places situa-
ted on the opposite meridian, it is consequently mid-
night.
Emily. To places situated equally distant from
these two meridians, it must then be six o'clock?
Mrs. B. Yes ; if they are to the east of the sun's
meridian it is six o'clock in the afternoon, because the
sun will have previously passed over them ; if to the
west, it is six o'clock in the morning, and the sun will
be {)roceeding towards that meridian.
Those circles which divide the globe into two
equal parts, such as the equator and the ecliptic, are
called greater circles ; to distinguish them from those
which divide it into two unequal parts, as the tropics
and polsyf circles, which are called lesser circles.
All circles are divided into 360 equal parts, called de-
grees, and degrees into 60 equal parts, called minutes.
The diameter of a circle is a right line drawn across
it, and passing through the centre ; for instance, the
boundary of this sphere is a circle, and its axis the di-
ameter of that circle ; the diameter is equal to a little
less than one third of the circumference. Can you
tell me nearly how many degrees it contains ?
Caroline. It must be something less than one third
of 360 degrees, or nearly 120 degrees.
Mrs. B. Right ; now Emily you may tell me
exactly how many degrees are contained in a meri-
dian ?
Emily. A meridian, reaching from one pole to the
other, is half a circle, and must therefore contain 180
degrees.
Mrs. B. Very well : and what number of degrees,
are there from the equator to the poles ?
118 ON THE EARTH.
Caroline. The equator being equally distant iVom
either pole, that distance must be half ofa meridian, or
a quarter of the circumference ofa circle, and con-
tain 90 degrees.
Mrs. B. Besides the usual division of circles into
degrees, the ecliptic is divided into twelve equal parts,
called signs, which bear the names of the constellations
through which this circle passes in the heavens.
The degrees measured on the meridians from north
to south, or south to north, are called degrees of la-
titude ; those measured from east to west on the
equator, the ecliptic, or any of the lesser circles, are
called degrees of longitude ; hence these circles
bear the name of longitudinal circles ; they are also
called parallels of latitude.
Emily. The degrees of longitude must then vary
in length according to the dimensions of the circle on
which they are reckoned ; those, for instance, at the
polar circles will be considerably smaller than those
at the equator ?
Mrs. B. Certainly ; since the degrees of circles
of different dimensions do not vary in number, they
must necessarily vary in length. The degrees of la-
titude, you may observe, never vary in length ; for
the meridians on which they are reckoned are all of
the same dimensions.
Emily. And of what length is a degree of latitude ?
Airs. B. Sixty geographical miles, which is equal
to 69i English statute miles.
Emily. The degrees of longitude at the equator
must then be of the same dimensions.
Mrs. B. They would, were the earth a perfect
sphere ; but its form is not exactly spherical, being
somewhat protuberant about the equator, and flat-
tened towards the poles. This form is supposed to
proceed from the superior action of the centrifugal
power at the equator.
Caroline. I thought I had understood the centri-
fugal force perfectly, but I do not comprehend its
e£tect in this instance.
ON THE EARTH. 119
Mrs. B. You know that the revolution of the
earth on its axis must give every particle a tenden-
cy to fly o£F from the centre, that this tendency is
stronger or weaker in proportion to the velocity with
which the particle moves ; now a particle situated
near one of the polar circles makes one rotation in
the same space of time as a particle at the equator ;
the latter, therefore, having a much larger circle to
describe, travels proportionally faster, consequently
the centrifugal force is much stronger at the equator
than at the polar circles : it gradually decreases as
you leave the equator and approach the poles, where,
as there is no rotatory motion, it entirely ceases.
Supposing, therefore, the earth to have been origi-
nally in u fluid state, the particles in the torrid zone
would recede much farther from the centre than
those in the frigid zones ; thus the polar regions
would become flattened, and those about the equator
elevated.
Caroline. I did not consider that the particles in
the neighbourhood of the equator move with greater
velocity than those about the poles ; this was the
reason I could not understand you.
Mrs. B. You must be careful to remember, that
those parts of a body which are farthest from the
centre of motion must move with the greatest velo-
city : the axis of the earth is the centre of its diur-
nal motion, and the equatorial regions the parts most
distant from the axis.
Caroline. My head then moves faster than my
feet ; and upon the summit of a mountain we are
carried round quicker than in a valley ?
Airs. B. Certainly, your head is more distant from
the centre of motion than your feet ; the mountain-
top than the valley : and the more distant any part
of a body is from the centre of motion, the larger is
the circle it will describe, and the greater therefore
must be its velocity.
Emily. I have been reflecting, that if the earth h
not a perfect circle
120 ON THE EARTtt.
Mrs. B. A sphere you mean, my dear ; a circle
is a round line, every part of which is equally distant
from the centre ; a sphere or globe is a round body,
the surface of which is every where equally distant
from the centre.
Emily. If, then, the earth is not a perfect sphere,
but prominent at the equator, and depressed at the
poles, would not a body weigh heavier at the equa-
tor than at the poles ; for the earth being thicker
at the equator, the attraction of gravity perpendicu-
larly downwards must be stronger.
Mrs. B. Your reasoning has some plausibility, but
I am sorry to, be obliged to add, that it is quite er-
roneous ; for the nearer any part of the surface of a
body is to the centre of attraction, the more strongly
it is attracted ; because the most considerable quan-
tity of matter is about that centre. In regard to its
effects, you might consider the power of gravity as
that of a magnet placed at the centre of attraction.
Emily. But were you to penetrate deep into the
earth, would gravity increase as you approached the
centre ?
Mrs. B. Certainly not ; 1 am referring only to
any situation on the surface of the earth. Were
you to penetrate into the interior, the attraction of the
parts above you would counteract that of the parts
Ijeneatli you, and consequently diminish the power
of gravity in proportion as you approached the cen-
tre ; and if you reached that point, being equally
attracted by the parts all around you, gravity would
cease, and you would b^ without weight.
Emily. Bodies then should weigh less at the
equator than at the poles, since they are more dis-
tant from the centre of gravity in the former than in
the latter situation ?
Mrs. B. And this is really the case ; but the dif-
ference of weight would be scarcely sensible, were it
not augmented by another circumstance.
Caroline. And what is this singular circumstance,
which seems to disturb the laws of nature ?
ON THE EARTH. 121
Mrs, B. One that you are well acquainted with,
as conducing more to the preservation than the de-
struction of order — the centrifugal force. This we
have just observed to be stronger at the equator ; and
as it tends to drive bodies from the centre, it is ne-
cessarily opposed to, and must lessen the power of
gravity, which attracts them towards the centre.
We accordingly find that bodies weigh lightest at the
equator, where the centrifugal force is greatest ; and
heaviest at the poles, where this power is least.
Carolinr. Has tlie experiment been made in these
different situations ?
Mrs. B, Lewis XIV., of France, sent philosophers
both to the equator and to Lapland for this purpose :
the severity of the climate, and obstruction of the ice,
has hitherto rendered every attempt to reach the
pole abortive ; but the difference of gravity at the
equator and in Lapland is very perceptible.
Caroline, Yet I do not comprehend, how the dif-
ference of weight could be ascertained ; for if the
body under trial decreased in weight, the weight
which was opposed to it in the opposite scale must
have diminished in the same proportion. For in-
stance, if a pound of sugar did not weigh so heavy at
the equator as at the poles, the leaden pound which
served to weigh it would not be so heavy either ;
therefore they would still balance each other, and the
different force of gravity could not be ascertained by
this means.
Mrs, B, Your observation is perfectly just : the
difference of gravity of bodies situated at the poles
and at the equator cannot be ascertained by weigh-
ing them ; a pendulum was therefore used for that
purpose.
Caroline, What, the pendulum of a clock ? how
could that answer the purpose ?
Mrs. B. A pendulum consists of a line, or rod, to
one end of which a weight is attached, and it is sus-
pended by the other to a fined point, about which it
is made to vibrate. Without being put in motion, a
11
122 ©N THE EARTHr
pendulum, like a plumb line, hangs perpendicular to
the general surface of the earth, by which it is at-
tracted ; but, if you raise a pendulum, gravity will
bring it back to its perpendicular position. It will,
however, not remain stationary there, for the veloci-
ty it has received during its descent will impel it on-
wards, and it will rise on the opposite side to an equal
height ; from thence it is brought back by gravity, and
again driven by the impulse of its velocity.
Caroline. If so, the motion of a pendulum would
be perpetual, and 1 thought you said, that there was
no perpetual motion on the earth.
Mrs. B. The motion of a pendulum is opposed
by the resistance of the air in which it vibrates, and
by the friction of the part by which it is suspended :
were it possible to remove these obstacles, the mo-
tion of a pendulum would be perpetual, and its vi-
brations perfectly regular ; being of equal distances,
and performed in equal times.
Emily. That is the natural result of the uniformi-
ty of the power which produces these vibrations, for
the force of gravity being always the same, the veloci-
ty of the pendulum must consequently be uniform.
Caroline. No, Emily, you are mistaken ; the cause
is not always uniform, and therefore the effect will
not be so either. I have discovered it, Mrs. B. ;
since the force of gravity is less at the equator than
at the poles, the vibrations of the pendulum will be
slower at the equfitor than at the poles.
Mrs. B. You are perfectly right, Caroline ; it
was by this means that the difference of gravity was
discovered, and the true figure of the earth ascer-
tained.
Emily. But how do they contrive to regulate
their time in the equatorial and polar regions ? for,
since in this part of the earth the pendulum of a
clock vibrates exactly once in a second, if it vibrates
faster at the poles and slower at the equator, the
inhabitants must regulate their clocks in a different
manner frem ours.
ON THE EARTH. 133
Mrs. B. The only alteration required is to length-
en the pendulum in one case, and to shorten it in the
other: for the velocity of the vibrations of a pendu-
lum depends on its length ; and when it is said that a
pendulum vibrates quicker at the pole than at the
equator, it is supposing it to be of the same length.
A pendulum which vibrates a second in this latitude
is 36k inches long. In order to vibrate at the equa-
tor in the same space of time, it must be lengthened
by the addition of a few lines ; and at the poles, it
must be proportionally shortened.
I shall now, I think, be able to explain to you
the variation of the seasons, and the difference of the
length of the days and nights in those seasons ; both
effects resulting from the same cause.
In moving round the sun, the axis of the earth is
not perpendicuhir to the plane of its orbit. Suppo-
sing this round table to represent the plane of the
earth's orbit, and this little globe, which has a wire
passing through it, representing the axis and poles,
we shall call the earth ; in moving round the table,
the wire is not perpendicular to it, but oblique.
Emily. Yes, I understand the earth does ftot go
round the sun in an upright position, its axis is slant-
ing or oblique.
Mrs. B. All the lines, which you learnt in your
last lesson, are delineated on this little globe ; you
must consider the ecliptic as representing the plane
of the earth's orbit; and the equator, which crosses
the ecliptic in two places, shows the degree of obli-
quity of the axis of the earth in that orbit, which is ex-
actly 23| degrees. The points in which the ecliptic
intersects the equator are called nodes.
But I believe I shall make this clearer to you by
revolving the little globe round a candle, which shall
represent the sun. (Plate IX. 6g. 2.)
As I now hold it, at A, you see it in the situation in
which it is in the midst of summer, or what is called
the summer solstice, which is on the Slst of June.
1:24 ON THE EARTH.
Emily. You hold the wire awry, I suppose, in oi--
ier to show that the axis of the earth is not upright '{
Mrs. B. Yes ; in summer, the north pole is incli-
ned towards the sun. In this season, therefore, the
northern hemisphere enjoys much more of his rays
than the southern. The sun, you see, now shines
over the whole of the north frigid zone, and notwith-
jstanding the earth's diurnal revolution, which I imi
tate hy twirling the ball on the wire, it will continue
to shine upon it as long as it remains in this situation,
whilst the south frigid zone is at tlie same time com-
pletely in obscurity.
Caroline. That is very strange : I never before
heard that there was constant day or night in any part
of the world! Mow mucli happier the inhabitants of
the north frigid zone must be than those of the south-
ern ; the first enjoy uninterrupted day, while the
last are involved in perpetual darkness.
Mrs. B. You judge with too much precipitation ;
examine a little further, and you will find, that the
two frigid zones share an equal fate.
We shall now make the earth set off from its posi-
tion in the siimmer solstice, and carry it round the
sun ; observe that the pole is always inclined in the
same direction, and points to the same spot in the
heavens. Tliere is a fixed star situated near that
spot, which is hence called the North Polar star.
Now let us stop the earth at B, and examine it in its
present situation ; it has gone through one quarter of
its orbit, and is arrived at that point at which the
ecliptic cuts or crosses the equator, and which is call-
ed the autumnal equinox.
Emily. That is then one of the nodes.
The sun now shines from one pole to the other,
just as it would constantly do, if the axis of the earth
were perpendicular to its orbit,
Mrs. B. Because the inclination of the axis is now
neither towards the sun nor in the contrary direction ;
at this period ef the year, therefore, the days and
nights are equal in every part of the earth. But the
UN THE EARTH. 1.25
uext Step she takes in her orbit, you see, involves the
north pole in darkness, whilst it illumines that of the
south ; this change was gradually preparing as 1 mo-
ved the earth from summer to autumn ; the arctic
circle, which was at tirst entirely illumined, began to
have short nights, which increased as the earth ap-
proached the autumnal equinox; and the instant it
passed that point, the long night of the north pole
commences, and the south pole begins to enjoy the
light of the sun. We shall now make the earth pro-
ceed in its orbit, and you may observe that as it ad-
vances, the days shorten, and the nights lengthen,
throughout the northern hemisphere, until it arrives
at the winter solstice^on the 21st of December, when
the north frigid zone is entirely in darkness, and the
southern has uninterrupted daylight.
Caroline. Then, after all, the sun, which I thought
so partial, confers his favours equally on all.
Mrs. B. Not so neither ; the inhabitants of the
torrid zone have much more heat than we have, aa
the sun's rays fall perpendicularly on them, while
they shine obliquely on the rest of the world, and al-
most horizontally on the poles ; for during their long
day of six months, the sun moves round their horizon
without either rising or setting; the only observable
difference is, that it is more elevated by a few de-
grees at midday, than at midnight.
Emily. To a person placed in the temperate zone,
in the situation in which we are in England, the sun
will shine neither so obliquely as it does on the poles,
nor so vertically as at the equator ; but its rays will
fall upon him more obliquely in autumn and winter,
than in summer.
Caroline. And, therefore, the inhabitants of the
temperate zones will not have merely one day and
one night in the year as happens at the poles, nor will
they have equal days and equal nights as at the equa-
tor ; but their days and nights will vary in length, at
different times of the year, according as their respec-
tive poles incline towards or from the sun, and the
11*
JiG ON THE EARTH.
difference will be greater in proportion to their dis-
tance from the equator.
Mrs. B, We shall now follow the earth through
the other half of her orbit, and you will observe, that
now, exactly the same effect takes place in the south-
ern hemisphere, as what we have just remarked in
the northern. Day commences at the south pole
when night sets in at the north pole ; and in every
other part of the southern hemisphere the days are
longer than the nights, while, on the contrary, our
eights are longer than our days. When the earth ar-
rives at the vernal equinox, D, where the ecliptic
again cuts the ei^uator, on the 26th of March, she is
situated, with respect to the sun, exactly in the same
position as in the autumnal equinox ; and the only
difference with respect to the earth is, that it is now
autumn in the southern hemisphere, whilst it is spring
with us.
Caroline. Then the days and nights are again
every where equal ?
Mrs. B. Yes, for the half of the globe which is
enlightened extends exactly from one pole to the
other ; the day breaks to the north pole, and the sun
sets to the south pole ; but in every other part of the
globe, the day and night is of twelve hours length,
hence the word equinox, which. is derived from the
Latin, meaning equal night.
As the earth proceeds towards summer, the days
lengthen in the northern hemisphere, and shorten in
the southern, till the earth reaches the summer sol-
stice, when the north frigid zone is entirely illumined,
and the southern is in complete darkness ; and we
have now brought the earth again to the spot from
whence we tirst accompanied her.
Emily. This is indeed a most satisf;\ctory expla-
nation of the seasons ; and the more I learn, the
more I admire the simplicity of means by which such
wonderful effects are produced.
Mrs. B. 1 know not which is most worthy of our
admiration, the cause, or the effect of the earth's re»
6N THE EARTH. 127
Tolution round the sun. The mind can find no ob-
ject of contemplation more sublime than the course
of this magnificent globe, impelled by the combined
powers of projection and attraction to roll in one in-
variable course around the source of light and heat:
and what can be more delightful than the beneficent
effects of this vivifying power on its attendant planet.
It is at once the grand principle which animates and
fecundates nature.
Emily. There is one circumstance in which this
little ivory globe appears to me to differ from the
earth ; it is not quite dark on that side of it which is
turned from the candle, as is the case with the earth
when neither moon nor stars are visible.
Mrs, B. This is owing to the light of the candle
being reflected by the walls of the room on every
part of the globe, consequently that side of the globe
on which the candle does not directly shine, is not in
total darkness. Now the skies have no walls to re-
flect the sun's light on that side of our earth which is
in darkness.
Caroline. I beg your pardon, Mrs. B., I think
that the moon and stars answer the purpose of walls
in reflecting the sun's light to us in the night.
Mrs. B. Very well, Caroline ; that is to say, the
moon and planets ; for the fixed stars, you know,
shine by their own light.
Emily. You say, that the superior heat of the
equatorial parts of the earth arises from the rays
falling perpendicularly on those regions, whilst they
fall obliquely on these more northern regions ; now
1 do not understand why perpendicular rays should
afford more heat than oblique rays.
Caroline. You need only hold your hand perpen-
dicularly over the candle, and then hold it sideways
obliquely, to be sensible of the difference.
Emily, I do not doubt the fact, but I wish to have
it explained.
Airs, B. You are quite right ; if Caroline had not
been satisfied with ascertaining the fact, without u!>*
5:^B ON THE KAHTtf.
derstanding it, she would not have brought forward
the candle as an illustration j the reason why 3'ou
feel so much more heat if you hold your hand per-
pendicularly over the candle, than if you hold it aide-
ways, is because a stream of heated vapour constantly
ascends from the candle, or any other burning body,
which being lighter than the air of the room, does
not spread laterally but rises perpendicularly, and
this led you to suppose that the rays were hotter in
the latter direction. Had you reflected, you would
have discovered that rays issuing from the candle
sideways, are no less perpendicular to your hand
when held opposite to them, than the rays which as-
cend when your hand is held over them.
The reason why the sun's rays afford less heat
when in an oblique direction than when perpendicu-
lar, is because fewer of them fall upon an equal por-
tion of the earth ; this will be understood better by
referring to Plate X. fig. 1, which represents two
equal portions of the sun's rays, shining upon difl'er-
ent parts of the earth. Here it is evident, that the
same quantity of rays fall on the space A B, as fall
on the space B C ; and as A B is less than B C, the
heat and light will be much stronger in the former
than in the latter; A B, you see, represents the
equatorial regions, where the sun shines perpendicu-
larly ; and B C, the temperate and frozen climates,
where his rays fall more obliquely.
Emily. This accounts not only for the greater
heat of the equatorial regions, but for the greater
heat of summer ; as the sun shines less obliquely ia
summer than in winter.
Airs. B. This you will see exemplified in figure
-2, in which the earth is represented as it is situated
*on the 21st of June, and England receives less oblique,
and consequently a greater number of rays, than at
any other season ; and figure 3, shows the situation
of England on the 21st of December, when the rays
*of the sun fall most obliquely upon her. But there
-*#- ako another reasoa why ..oblique rays give le«s
m. J.
Tiif- 4.
ON THE EARTH* 123
keat than perpendicular rays ; which i^, that they
have a greater portion of the atmosphere to traverse ;
and though it is true that the atmosphere i« itself a
transparent body, freely admitting the passage of the
sun's rays, yet it is always loaded more or less with
dense and foggy vapour, which the rays of the sun
cannot easily penetrate ; therefore the greater the
quantity of atmosphere the sun's rays have to pass
through in their way to the earth, the less heat they
will retain when they reach it. 'J'his will be better
\inderstood by rt^ferring to fig. 4. The dotted line
round the earth describes the extent of the atmos-
phere, and the lines which proceed from the sun to
the earth the passage of two equal portions of the
sun's rays to the equatorial and polar regions ; the
latter, you see, from its greater obliquity passes
through a greater extent of atmosphere.
Caroline. And this, no doubt, is the reason why
the sun in the morning and the evening gives so much
less heat than at midday.
Mrs. B. The diminution of heat, morning and
evening, is certainly owing to the greater obliquity
of the sun's rays ; and as such they are affected by
both the causes which I have just explained to you ;
the difficulty of passing through a foggy atmosphere is
perhaps more particularly applicable to them, as
mists and vapours are very prevalent about the time
of sunrise and sunset. But the diminished obliquity
of the sun's rays is not the sole cause of the heat of
summer ; the length of the days greatly conduces to
it ; for the longer the sun is above the horizon, the
more heat he will communicate to the earth.
Caroline. Both the longest days, and the most per-
pendicular rays, are on the 21st of June ; and yet the
greatest heat prevails in July and August.
Mrs. B. Those parts of the earth which are once
heated, retain the heat for some length of time, and
the additional heat they receive, occasions an eleva-
tion of temperature, although the days begin to short-
en, and the sun's rays to fall more obliquely. For
130 ©N THE EARTH.
the same reason, we have generally more heat ai
three o'clock in the afternoon, than at twelve, when
the sun is on the meridian.
Emily. And pray, have the other planets the same
vicissitudes of seasons as the earth ?
- Mrs. B. Some of them more, some less, accord-
ing as their axes deviate more or less from the per-
pendicular to the plane of their orbits. The axis of
Jupiter is nearly perpendicular to the plane of his or-
bit ; the axes of Mars and of Saturn are each inclined
at angles of about sixty degrees ; whilst the axis of
Venus is believed to be elevated only fifteen or twenty
degrees above her orbit ; the vicissitudes of her sea-
sons must theretbre be considerably greater than
ours. For further particulars respecting the planets,
I shall refer you to Bonnycastle's Introduction to
Astronomy.
1 have but one more observation to make to you
relative to the earth's motion, which is, that although
we have but 365 days and nights in the year, she per-
forms 366 complete revolutions on her axis during
that time.
Caroline. How is that possible ? for every com-
plete revolution must bring the same place back to
the sun. It is^novv just twelve o'clock, the sun is,
therefore, on our meridian ; in twenty-four hours
will it not be returned to our meridian again, and will
not the earth have made a complete rotation on its
axis ?
Mrs. B. If the earth had no progressive motion
in its orbit whilst it revolves on its axis, this would
be the case ; but as it advances almost a degree west-
ward in its orbit, in the same time that it completes
a revolution eastward on its axis, it must revolve
nearly one degree more in order to bring the same
meridian back to the sun.
Caroline. Oh, yes ! it will require as much more
of a second revolution to bring the same meridian
back to the sun, as is equal to the space the earth
ON THE EARTH. 131
has advanced in her orbit, that is, nearly a degree ;
this difference is, however, very little.
Mrs. B. These small daily portions of rotation are
each equal to the three hundred and sixty-fifth part
of a circle, which at the end of the year amounts to
one complete rotation.
Emily. That is extremely curious. If the earth,
then, had no other than its diurnal motion, we should
have 366 days in the year.
Mrs B. We should have 366 days in the same
period of time that we now have 365 : but if we did
not revolve round the sun, we should have no na-
tural means of computing years.
You will be surprised to hear, that if lime is calcu-
lated by the stars instead of the sun, the irregularity
which we have just noticed does not occur, and that
one complete rotation of the earth on its axis, brings
the same meridian back to any fixed star.
Emily. That seems quite unaccountable ; for the
earth advances in her orbit with regard to the fixed
stars, the same as with regard to the sun.
Mrs. B. True, but then the distance of the fixed
stars is so immense, that our solar system is in com-
parison to it but a spot, and the whole extent of the
earth's orbit but a point ; therefore, whether the
earth remained stationary, or whether it revolved in
its orbit durins; its rotation on its axis, no sensible dif-
ference would be produced with regard to the fixed
stars. One complete revolution brings the same
meridian back to the same fixed star ; hence the fix-
ed stars appear to go round the earth in a shorter
time than the sun by three minutes fifty-six seconds
of time.
Caroline. These three minutes fifty-six seconds is
the time which the earth takes to perform the addi-
tional three hundred and sixty-fifth part of the circle,
in order to bring the same meridian back to the sun.
Mrs. B. Precisely. Hence the j^tars gain every
<Jay three minutes fifty-six seconds on the sun, which
13ii »N THK EARTH.
makes them rise that portion of time earlier erery
day.
When time is calculated by the stars it is called
sidereal time, when by the sun solar or apparent time.
Caroline. Then a sidereal day is three minutes
fifty-six seconds shorter than a solar day of twenty-
four hours.
Mrs. B. I must also explain to you what is meant
by a sidereal year.
The common year, called the solar or tropical
year, containing 363 days, five hours, forty-eight
minutes, and fifty-two seconds, is measured from the
time the sun sets out from one of the equinoxes, or
solstices, till it returns to the same again ; but this
year is completed before the earth has finished one
entire revolution in its orbit.
Emily. I thought that the earth performed one
complete revolution in its orbit every year ; what is
the reason of this variation ?
Mrs. B. It is owing to the spheroidal figure of the
earth. The elevation about the equator produces
much the same effect as if a similar mass of matter,
collected in the form of a moon, revolved round the
equator. When this moon acted on the earth in con-
junction with or in opposition to the sun, variations
in the earth's motions would be occasioned, and these
variations produce what is called the precession of
the equinoxes.
Emily. What does that mean ? I thought the equi-
noctial points, or nodes, were fixed points in the
heavens, in which the equator cuts the ecliptic.
Mrs. B. These points are not quite fixed, but
have an apparently retrograde motion, that is to say,
instead of being every revolution in the same place,
they move backwards. Thus, if the vernal equinox
is at A, (fig. 1. plate XI.) the autumnal one will be
at B instead of C, and the following vernal equinox
at D instead of at A, as would be the case if the
equinoxes were stationary at opposite points of the
earth's orbit.
PLATE ja.
©N THE EARTH. 13;^
Caroline. So that when the earth moves from one
equinox to the other, though it takes half a year to
perform the journey, it has not travelled through
half its orbit.
Mrs. B. And, consequently, when it returns again
to the first equinox, it has not completed the whole
of its orbit. In order to ascertain when the earth
has performed an entire revolution in its orbit, we
must observe when the sun returns in conjunction
with any fixed star ; and this is called a sidereal year.
Supposing a fixed star situated at E, (fig. 1. plate
XI.) the sun would not appear in conjunction with
it till the earth had returned to A, when it would
have completed its orbit.
Emily. And how much longer is the sidereal than
the solar year ?
Mrs. B. Only twenty minutes ; so that the varia-
tion of the equinoctial points is very inconsiderable.
I have given them a greater extent in the figure in
order to render them sensible.
In regard to time, I must further add, that the
earth's diurnal motion on an inclined axis, together
with its annual revolution in an elliptic orbit, occa-
sions so much complication in its motion, as to pro-
duce many irregularities ; therefore, true equal time
cannot be measured by the sun. A clock, which was
always perfectly correct, would in some parts of tlie
year be before the sun, and in other parts after it.
There are but four periods in which the sun aud a
perfect clock would agree, which is the 16th of
April, the 16th of June, the 23d of August, and the
24th of December.
Emily. And is there any considerable difference
between solar time and true time ?
Mrs. B. The greatest difference amounts to be-
tween fifteen and sixteen minutes. Tables of equa-
tion are constructed for the purpose of pointing out
and correcting these differences between solar time
and equal or mean time, which is the denomination
given by astronomers to true time.
12
CONVERSATION IX.
ON THE MOON.
Of the Mooii^s Motion. — Phases of the Moon. — Eclip-
ses of the Moon. — Eclipses of Jupiter^s Moons. —
Of the Latitude and Longitude. — Of the Transits of
the Inferior Planets. — Of the Tides.
MRS. B. We shall to-day confine our attention to
the moon, which offers many interesting phenomena.
The moon revolves round the earth in the space of
about twenty-nine days and a half, in an orbit nearly
parallel to that of the earth, and accompanies us in
our revolution round the sun.
Emily. Her motion, then, must be rather of a
complicated nature ; for as the earth is not stationary,
but advances in her orbit whilst the moon goes round
her, the moon must proceed in a sort of progressive
circle.
Mrs. B. That is true ; and there are also other
circumstances which interfere with the simpUcity and
regularity of the moon's motion, but which are too
intricate for you to understand at present.
The moon always presents the same face to us, by
which it is evident that she turns but once upon her
axis, while she performs a revolution round the earth;
so that the inhabitants of the moon have but one day
and one night in the course of a lunar month.
Caroline. We afford them, however, the advan-
tage of a magnificent moon to enlighten their long
nights.
ON THE MOON. 135
Mrs. B. That advantage is but partial ; for since
we always see the same hemisphere of the moon, the
inhabitants of that hemisphere alone can perceive us.
Caroline, One half of the moon then enjoys our
light every night, while the other half has constantly
nights of darkness. If there are any astronomers in
those regions, they would doubtless be tempted to
visit the other hemisphere, in order to behold so
grand a luminary as we must appear to them. But,
pray, do they see the earth under all the changes
which the moon exhibits to us ?
Mrs. B. Exactly so. These changes are called
the phases of the moon, and require some explana-
tion. In fig. 2, plate XI. let us say that S represents
the sun, E the earth, and A B C D the moon in dif-
ferent parts of her orbit. When the moon is at A,
her dark side being turned towards the earth, we
shall not see her as at a ; but her disappearance is of
very short duration, and as she advances in her orbit
we perceive her under the form of a new moon ;
when she has gone through one eighth of her orbit at
B, one quarter of her enlightened hemisphere will
be turned towards the earth, and she will then appear
horned as at b: when she has performed one quarter
of her orbit, she shows us one half of her enlighten-
ed side as at c ; at d she is said to be gibbous, and at
e the whole of the enlightened side appears to us,
and the moon is at full. As she proceeds in her or-
bit she becomes again gibbous, and her enliglitened
hemisphere turns gradually away from us till she
completes her orbit and disappears, and then again
resumes her form of a new moon.
When the moon is at full, or a new moon, she is
said to be in conjunction with the sun, as they are
then both in the same direction witli regard to the
earth ; when at her quarters she is said to be in op-
position to the sun.
Etnily. Are not the eclipses produced by the moon
passing between the sun and the earth ?
Mrs. B. Yes ; when the moon passes between the
ftun and the earth, she intercepts his rays, or, in other
136 ®N THE MOON.
words, casts a shadow on the earth, then the sun is,
eclipsed, and the daylight gives phice to darkness,
while the moon's shadow is passing over us.
When, on the contrary, the earth is between the
sun and the moon, it is we who intercept the sun's
rays, and cast a shadow on the moon ; the moon is
then darkened, she disappears from our view, and
is eclipsed.
Emily. But as the moon goes round the earth
every month, she must be once during that time
between the earth and the sun, and the earth must
likewise be once between the sun and the moon,
and yet we have not a solar and a lunar eclipse every
month ?
Mrs. B. The orbits of the earth and moon are
not exactly parallel, but cross or intersect each other;
and the moon generally passes either above or below
the earth when she is in conjunction with the sun,
and does not therefore intercept the sun's rays, and
produce an eclipse ; for this can take place only when
the earth and moon are in conjunction in that part of
their orbits which cross each other, (called the nodes
of their orbits,) because it is then only, that they are
both in a right line with the sun.
Emily. And a partial eclipse takes place, I sup-
pose, when the moon, in passing by the earth, is not
sufficiently above or below the earth's shadow en-
tirely to escape it ?
Mrs. B. Yes, one edge of her disk then dips into
the shadow, and is eclipsed ; but as the earth is
larger than the moon, when the eclipse happens
precisely at the nodes, they are not only total, but
last for some length of time.
When the sun is eclipsed, the total darkness is
confined to one particular part of the earth, evident-
ly showing that the moon is smaller than the earth,
since she cannot entirely skreen it from the sun. In
fig. 1, pi. XII. you will find a solar eclipse describ-
ed ; S is the sun, M the moon, and E the earth ; and
the moon's shadow, you see, is not large enough to
FLATS JOI
ON THE MOON, 1^7
cover the earth. The lunar eclipses, on the contra-
ry, are visible from every part of the earth, where
the moon is above the horizon ; and we discover, by
the length of time which the moon is in passing
through the earth's shadow, that it would be suffi-
cient to eclipse her totally, were she 47 times her
actual size ; it follows, therefore, that the earth is
47 times the size of the moon.
In fig. *£. S represents the sun, which pours forth
rays of light in straight lines in every direction. E
is the earth, and M the moon. Now a ray of light
coming from one extremity of the sun's disk in the
direction A B, will meet another coming from the op-
posite extremity in the direction C B ; the shadow of
the earth cannot therefore extend beyond B ; as the
sun is larger than the earth, the shadow of the latter
is conical, or the figure of a sugar loaf ; it gradually
diminishes, and is much smaller than the earth where
the moon passes through it, and yet we find the moon
to be not only totally eclipsed, but some length of
time in darkness, and hence we are enabled to ascer-
tain its real dimensions.
Emily. When the moon eclipses the sun to us, we
must be eclipsed to the moon ?
Mrs. B. Certainly; for if the moon intercepts the
sun's rays, and casts a shadow on us, we must neces-
sarily disappear to the moon, but only partially, as in
fig. 1.
Caroline There must be a great number of eclip-
ses in the distant planets, which have so many moons ?
Mrs. B. Yes, few days pass without an eclipse
taking place : for among the number of satellites, one
or other of them are continually passing either be-
tween their planet and the sun, or between the planet
and each other. Astronomers are so well acquainted
with the motion of the planets and their satellites, that
they have calculated not only the eclipses of our
moon, but those of Jupiter, with such perfect accu-
racy, that it has aflbrded a means of aiscertaining the
longitude.
12*
138 ON THE MOON.
Caroline. But is it not very easy to find both the
latitude and longitude of any place by a map or globe '.
Mrs. B If you know where you are situated,
there is no difficulty in ascertaining the latitude or
longitude of the place by referring to a map ; but
supposing that you had been a length of time at sea,
interrupted in your course by storms, a map would
afford you very little assistance in discovering where
you were.
Caroline. Under such circumstances, I confess I
should be equally at a loss to discover either latitude
or longitude.
Mrs. B. The latitude may be easily found by ta-
king the altitude of the pole ; that is to say, the
number of degrees that it is elevated above the hori-
zon, for the pole appears more elevated as we ap-
proach it, and less as we recede from it.
Caroline. But unless you can see the pole how
can you take its altitude ?
Mrs. B. The north pole points constantly towards
one particular part of the heavens, in which a star
is situated, called the Polar Star ; this star is visible on
clear nights, from every part of the northern hemis-
phere; the altitude of the polar star, is therefore the
same number of degrees as that of the pole ; the
latitude may also be determined by observations made
on the sun or any of the fixed stars ; the situation
therefore of a vessel at sea, with regard to north and
south, is easily ascertained. The ditficulty is respect-
ing east and west, that is to say, its longitude. As we
have no eastern poles from which we can reckon our
distance, some particular spot must be fixed upon
for that purpose. The English reckon from the
meridian of Greenwich, where the royal observatory
is situated ; in French maps you will find that the
longitude is reckoned from Paris.
The rotation of the earth on its axis in 24 hours
iVom west to east occasions, you know, an apparent
motion of the sun and stars in the contrary direction,
and the sun appears to go round the earth in the space
ON THE MOO-V. 139
i)( 24 hours, passing over fifteen degrees, or a twenty-
fourth part of the earth's circumference every hour;
therefore, when it is twelve o'clock in London, it is
one o'clock in any place situated fifteen degrees to
the east of London, as the sun must have passed the
meridian of that place an hour before he reaches that
of London. For the same reason it is eleven o'clock
to any place situated fifteen degrees to west of Lon-
don, as the sun will not come to that meridian till an
hour later.
If then the captain of a vessel at sea, could know
precisely what was the hour at London, he could, by
looking at his watch, and comparing it with the hour
of the spot in which he was, ascertain the longitude.
Emily. But if he had not altered his watch, since
he sailed from London, it would indicate the hour it
was then in London.
Mrs. B. True ; but in order to know the hour of
the day of the spot in which he is, the captain of a
vessel regulates his watch by the sun when it reaches
the meridian.
Emily. Then if he had two watches, he might
keep one regulated daily, and leave the other unalter-
ed ; the former would indicate the hour of the place
in which he was situated, and the latter the hour of
London ; and by comparing them together, he would
be able to calculate his longitude.
Mrs. B. You have discovered, Emily, a mode of
finding the longitude, which I have the pleasure to
tell you, is universally adopted : watches of a supe-
rior construction, called chronometers, or time-keep-
ers, are used for this purpose ; but the best watches
are liable to imperfections, and should the time-keep-
er go too fast or too slow, there would be no means of
ascertaining the error ; implicit reliance cannot con-
sequently be placed upon them.
Recourse is therefore had to the eclipses of Jupi-
ter's satellites. A table is made of the precise time
at which the several moons are echpsed to a specta-
iov at London j when they appear eclipsed to a spec-
140 ON THE MOON.
tator in any other spot, he may, by consulting the ta-
ble, know what is the hour at London ; for the eclipse
is visible at the same moment from whatever place
on the earth it is seen. He has then only to look at
the watch, which points out the hour of the place Iq
which he is, and by observing the difference of time
there, and at London, he may immediatel)' determine
his longitude.
Let us suppose, that a certain moon of Jupiter is
always eclipsed at six o'clock in the evening ; and
that a man at sea consults his watch, and tinds that it
is ten o'clock at ni^hi, where he is situated, at the
moment the eclipse takes place ; what will be big
longitude ?
Emily. That is four hours later than in London :
four times fifteen degrees make 60 ; he would, there-
fore, be sixty degrees east of London, for the sun
most have passed his meridian before it reaches that
of London.
Mrs. B. For this reason the hour is always later
than London, when the place is east longitude, and
earlier when it is west longitude. Thus the longitude
can be ascertained whenever the eclipses of Jupiter's
moons are visible.
But it is not only the secondary planets which pro-
duce eclipses, for the primary planets near the sun
eclipse him to those at a greater distance when they
come in conjunction in the nodes of their orbits ; but
as the primary planets are much longer in performing
their course round the sun, than the satellites in going
round their primary planets, these eclipses very sel-
dom occur.
Mercury and Venus have however passed in a
right line between us and the sun, but being at so
great a distance from us, their shadows did not ex-
tend so far as the earth ; no darkness was therefore
produced on any part of our globe ; but the planet
appeared like a small black spot, passing across the
sun's disk ; this is called a transit of the planet.
It was by the last transit of Venus, that astronO-
ON THE MOON. 141
mers were enabled to calculate with some degree of
accuracy the distance of the earth from the sun, and
the dimensions of the latter.
Emily. 1 have heard that the tiSes are affected
by the moon, but I cannot conceive what influence it
can have on them.
Mrs. B. They are produced by the moon's at-
traction, which draws up the waters in a protu-
berance.
Caroline. Does attraction act on water more pow-
erfully than on land ? I should have thought it would
have been just the contrary, for land is certainly a
more dense body than water?
Mrs. B. Tides do not arise from water bein^
more strongly attracted than land, for this certainly is
not the case ; but the cohesion of fluids being much
less than that of solid bodies, they more easily yield
to the power of gravity, in consequence of which
the waters immediately below the moon are drawn
up by it in a protuberance, producing a full tide, or
what is commonly called high water, at the spot
where it happens. So far the theory of the tides
is not difficult to understand.
Caroline. On the contrary, nothing can be more
simple : the waters, in order to rise up under the
moon, must draw the waters from the opposite side
of the globe, and occasion ebb-tide, or low water in
those parts.
Mrs. B. You draw your conclusion rather too
hastily, my dear ; for, according to your theory, we
should have full tide only once in twenty-four hours,
that is, every time that we were below the moon,
%vhile we find that we have two tides in the course of
twenty-four hours, and that it is high-water with us
and with our antipodes at the same time.
Caroline. Yet it must be impossible for the moon
to attract the sea in opposite parts of the globe, and
in opposite directions at the same time.
Mrs. B. This opposite tide is rather more diffi-
cult to explain, than that which is drawn up beneath
142 ON THE MOON.
the moon ; with a little attention, however, I hope I
shall be able to make you understand it.
You recollect that the earth and moon are mutual-
ly attracted towards a point, their common centre of
gravity and of motion ; can you tell me what it is that
prevents their meeting and uniting at this point ?
Emily. Their projectile force, which gives them a
tendency to fly from this centre.
Mrs. B. And is hence called their centrifugal
force. Now we know that the centrifugal force in-
creases in proportion to the distance from the centre
of motion.
Caroline. Yes, I recollect your explaining that
to us, and illustrating it by the motion of the flyers
oi a wind-mill, and the spinning of a top.
Emily. And it was but the other day you showed
us that bodies weighed less at the equator than in the
polar regions, in consequence of the increased cen-
trifugal force in the equatorial parts.
Mrs. B. Very well. The power of attraction,
on the contrary, increases as the distance from the
centre of gravity diminishes ; when, therefore, the
two centres of gravity and of motion are in the same
spot, as is the case with regard to the moon and the
earth, the centrifugal power and those of attraction
will be in inverse proportion to each other ; that is
to say, where the one is strongest the other will be
weakest.
Emily. Those parts of the ocean, then, which are
most strongly attracted, will have least centrifugal
force ; and those parts which are least attracted, will
have the greatest centrifugal force.
Mrs. B. In order to render the question more
simple, let us suppose the earth to be every where
covered by the ocean, as represented in fig. S. PI.
XII. M is the moon, ABC D the earth, and X the
common centre of gravity and of motion of these
two planets. Now the waters on the surface of the
earth, about A, being more strongly attracted than
any other part, will be elevated ; the attraction of the
9N THE MOON. 143
moon at B and C being less, and at D least of all.
But the centrifugal force at D will be greatest, and the
waters there will in consequence have the greatest
tendency to recede from the moon ; the waters at B
and C will have less tendency to recede, and at A
least of all. The waters, therefore, at D, will re-
cede furthest, at the same time that they are least at-
tracted, and in consequence will be elevated in a pro-
tuberance similar to that at A.
Emily. The tide A, then, is produced by the
moon's attraction, and increased by the feebleness of
the centrifugal power in those parts ; and the tide D
is produced by the centrifugal force, and increased
by the feebleness of the moon's attraction in those
parts.
Caroline. And when it is high water at A and D,
it is low water at B and C : now I think I compre-
hend the nature of the tides again, though 1 confess
it is not quite so easy as I at first thought.
But, Mrs. B., why does not the sun produce tides
as well as the moon ; for its attraction is greater than
that of the moon ?
Mrs. B. It would be at an equal distance, but our
vicinity to the moon makes her influence more pow-
erful. The sun has, however, a considerable effect
on the tides, and increases or diminishes them as it
acts in conjunction with, or in opposition to the moon.
Emily. I do not quite understand that.
Mrs. B. The moon is a month in going round the
earth ; twice during that time, therefore, at full and
at change, she is in the same direction as the sun, both
then act in conjunction on the earth, and produce
very great tides, called spring tides, as described in
fig. 4, at A and B ; but when the moon is at the in-
termediate parts of her orbit, the sun, instead of af-
fording assistance, weakens her power, by acting in
opposition to it ; and smaller tides are produced,
called neap tides, as represented in fig. 5.
Emily. I have often observed the difference of
these tides when I have been at the sea side.
But fiince attraction is mutual between the moon
144 •on TflE MOON.
and the earth, we must produce tides in the moon ;
and these must be more considerable in proportion as
our planet is larejer. And yet the moon does not ap-
pear of an oval form.
Mrs. B. You must recollect, that in order to ren-
der the explanation of the tides clearer, we supposed
the whole surface of the earth to be covered with the
ocean ; but that is not really the case, either with
the earth or the moon, and the land which intersects
the water destroys the regularity of the effect.
Caroline. True ; we may, however, be certain,
that whenever it is high water the moon is immediate-
ly over our heads.
Mrs. B. Not so, either; for as a similar effect is
produced on that part of the globe immediately be-
neath the moon, and on that part most distant from it,
it cannot be over the heads of the inhabitants of both
those situations at the same time. Besides, as the
orbit of the moon is very near'y parallel to that of
the earth, she is never vertical but to the inhabitants
of the torrid zone ; in that climate, therefore, the tides
are greatest, and they diminish as you recede from it
and approach the poles.
Caroline. In the torrid zone, then, I hope you
will grant that the moon is immediately over, or op-
posite the spots where it is high water?
Mrs. B. I cannot even admit that; for the ocean
naturally partaking of the earth's motion, in its rota-
tion from west to east, the moon, in forming a tide,
has to contend against the eastern motion of the waves.
All matter, you know, by its inertia, makes some re-
sistance to a change of state ; the waters, therefore,
do not readily yield to the attraction of the moon, and
the effect of her influence is not complete till three
hours after she has passed the meridian, where it is
full tide.
Emily. Pray what is the reason that the tid^ is
three quarters of an hour later every day?
Mrs. B. Because it is twenty-four hours and three
quarters before the same meridian on our globe re-
OP THE MOON. 14i
turns beneath the moon. The earth revolves on its
axis in about twenty-four h^^urs ; if the moon were
stationary, therefore, the same part of our globe
would, every twenty-four hours, return beneath the
moon; but as durinj; our daily revolution the moon
advances in her orbit, the earth must make more than
a complete rotation in order to brin^ the same meri-
dian opposite the moon: we aie three quarters of an
hour in overtaking her. The tides, therefore, are
retarded for the same reason that the moon rises later
by three quarters of an hour every day.
We have now, I think, concluded the observations
I had to make to you on the subject of astronomy ; at
<yur next interview, I shall attempt to explain to you
*he elements of hydrostatics.
13
CONVERSATION X.
ON THE MECHANICAL PROPERTIES
OF FLUIDS.
Definition of a Fluid. — Distinction between Fluids and
Liquids. — Of JVon- Elastic Fluids. — Scarcely Suscep-
tible of Compression. — Of the Cohesion of Fluids. —
Of (heir Gravitation. — Of their Equilibrium. — Of
their Pressure. — Of Specific Gravity. — Of the Speci-
fic Gravity of Bodies Heavier than Water. — Of those
of the Same Weight as Water. — Of those Lighter than
Water, — Of the Specific Gravity of Fluids.
MRS. B. We have hitherto confined our attention
fo the noechanical properties of solid bodies, which
have been illustrated, and, 1 hope, thoroughly im-
pressed upon your memory, by the conversations we
have subsequently had on astronomy. It will now be
necessary for me to give you some account of the me-
chanical properties of fluids — a science which is call-
ed hydrostatics. A fluid is a substance which yields
to the slightest pressure. If you dip your hand into
a basin of water, you are scarcely sensible of meeting
with any resistance.
Emily. The attraction of cohesion is, then, I sup-
pose, less powerfHl in fluids than in solids ?
Airs. B, Yes ; fluids, generally speaking, are bo-
dies of less density than solids. From the slight co-
hesion of the particles of fluids, and the facility with
which they slide over each other, it is inferred, that
they must be small, smooth, and globular; smooth,
beeause there appears to be little or no frictioB among
MECHANICAL PROPERTIES OF FLUIDS. 147
them, and globular, because touching each other but
by a point would account for the slightness of their
cohesion.
Caroline. Pray what is the distinction between a
fluid and a liquid ?
Mrs. B. Liquids comprehend only one class of
fluids. There is another class distinguished by the
name of elastic fluids, or gases, which comprehends
the air of the atmosphere, and all the various kinds of
air with which you will become acquainted when you
study chemistry. Tlieir mechanical properties we
shall examine at our next meeting, and confine our
attention this morning to those of liquids, or non-elas-
tic fluids.
Water, and liquids in general, are scarcely suscep-
tible of being compressed, or squeezed into a small-
er space than that which they naturally occup3^
This is supposed to be owing to the extreme minute-
ness of their particles, which, rather than submit to
compression, force their way through th^ pores of
the substance which confines them. This was shown
by a celebrated experiment, made at Florence many
.years ago. A hollow globe of gold was filled with
water, and on its being submitted to great pressure,
the water was seen to exude through the pores of
the gold, which it covered with a fine dew. Fluids
gravitate in a more perfect manner than solid bodies ;
for the strong cohesive attraction of the particles of
the latter in some measure counteracts the eff"ect of
gravity. In this table, for instance, the cohesion of
the particles of wood enables four slender legs to
support a considerable weight. Were the cohesion
destroyed, or, in other words, the wood converted
into a fluid, no support could be afl'orded by the legs,
for the particles no longer cohering together, each
would press separately and independently, and would
be brought to a level with the surface of the earth.
Emily. This want of cohesion is then the rea-
son why fluids can never be formed into figures, or
maintained in heaps ; for though it is true the wind
i48 MECHANICAL PROPERTIES OF FLUIDS.
raises water into waves, they are immediately after-
wards destroyed by gravity, and water always finds
its level.
Mrs. B, Do you understand what is meant by the
level, or equilibrium of fluids ?
Emily. I believe 1 do, though I feel rather at a
loss to explain it. Is not a fluid level when its sur-
face is smooth and flat, as is the case with all fluids
when in a state of rest ?
Mrs. B. Smooth, if you please, but not flat; for
the definition of the equilibrium of a fluid is, that
every part of the surface is equally distant from the
point to which gravity tends, that is to say, from the
centre of the earth ; hence the surface of all fluids
must be bulging, not flat, since they will partake of
the spherical form of the globe. This is very evi-
dent in large bodies of water, such as the ocean, but
the sphericity of small bodies of water is so trifling,
that their surfaces appear flat.
This level, or equilibrium of fluids, is the natural
result of their particles gravitating independently of
each other ; for when any particle of a fluid acci-
dentally finds itself elevated above the rest, it is at-
tracted down to the level of the surface of the fluid,
and the readiness with which fluids yield to the
slightest impression, will enable the particle by its
weight to penetrate the surface of the fluid and mix
with it.
CaroUnf. But I have seen a drop of oil float ob
the surface of water without mixing with it.
Mrs, B. That is, because oil is a lighter liquid
than water. If you were to pour water over it, the
oil would rise to the surface, being forced up by the
superior gravity of the water. Here is an instru-
ment called a water-level, (fig. 1. plate XIII.) which
is constructed upon the principle of the equilibrium
of fluids. It consists of a short tube, A B, closed at
both ends, and containing a little water ; when the
tube is not perfectly horizontal the water runs to the
lower end, and it is by this means that the level of
Fi:if. s.
PLATE. Xm.
MECHANICAL PROPERTIES Or FLUIDS. 149
any situation, to which we apply the instrument, is
ascertained.
SoHd bodies you may, therefore, consider as gra-
vitating in masses, for the strong cohesion of their
particles makes them weigh altogether, while every
particle of a fluid may be considered as composing
a separate mass, gravitating independently of each
other. Hence the resistance of a fluid is considera-
bly less than that of a solid body ; for the resistance
of the particles acting separately, they are more
easily overcome.
Emily. A body of water, in falling, does certainly
less injury than a solid body of the same weight.
Mrs. B. The particles of fluids acting thus inde-
pendently, press against each other in every direc-
tion, not only downwards but upwards, and laterally
or sideways ; and in consequence of this equality of
pressure, every particle remains at rest in the fluid.
If you agitate the fluid you disturb this equality of
pressure, and the fluid will not rest till its equili-
brium is restored.
Caroline. The pressure downwards is very natu-
ral ; it is the effect of gravity, one particle weighing
upon another presses on it ; but the pressure side-
ways, and particularly the pressure upwards, I can-
not understand.
Mrs. B. If there were no lateral pressure, water
would not run out of an opening on the side of a
vessel. If you fill a vessel with sand, it will not run
out of such an opening, because there is scarcely
any lateral pressure among its particles.
Emily. When water runs out of the side of a ves-
sel, is it not owing to the weight of the water above
the opening ?
Mrs. B. If the particles of fluids were arranged
in regular columns thus, (fig. 2,) there would be no
lateral pressure, for when one particle is perpen-
dicularly above the other, it can only press it down-
wards ; but as it must continually happen, that a par-
ticle presses between two particles beneath, (fig. 3,)
these last must suffer a lateral pressure.
13*
150 MECHANICAL PROPERTIES OF FLtJIDSf.
Emily. The same as when a wedge is driven into
a piece of wood, and separates the parts laterally,
Mrs. B. Yes. The lateral pressure proceeds,
therefore, entirely from the pressure downwards, or
the weight of the liquid above ; and consequently
the lower the orifice is made in the vessel, the great-
er will be the velocity of the water rushing out of it.
Here is a vessel of water (fig. 4) with three stop
cocks at different heights ; we shall open them, and
you will see with what different degrees of velocity
the water issues from them. Do you understand
this, Caroline ?
Caroline. Oh, yes. The water from the upper
spout receiving but a slight pressure, on account of
its vicinity to the surface, flows but gently ; the
second cock having a greater weight above it, the
water is forced out with greater velocity, whilst the
lowest cock, being near the bottom of the vessel, re-
ceives the pressure of almost the whole body of wa-
ter, and rushes out with the greatest impetuosity.
Mrs. B. Very well : and you must observe, that
as the lateral pressure is entirely owing to the pres-
sure downwards, it is not effected by the horizontal
dimensions of the vessel, which contains the water,
but merely by its depth ; for as every particle acts
independently of the rest, it is only the column of
*j)articles immediately above the orifice that can weigh
upon and press out the water.
Emily. The breadth and width of the vessel then
oun, be of no consequence in this respect. The late-
ral pressure on one side, in a cubical vessel, is, I sup-
pose, not so great as the pressure downwards.
Mrs. B. No : in a cubical vessel, the pressure
downwards will be double the lateral pressure on
one side ; for every particle at the bottom of the
vessel is pressed upon by a column of the whole
depth of the fluid, whilst the lateral pressure dimi-
nishes from the bottom upwards to the surface, where
the particles have no pressure.
Caroline, A:»d from whence proceeds the pr€£-
MECHANICAL PROPERTIES OP FLUIDS. 161
sure of fluids upwards ? that seems to me the most
unaccountable, as it is in direct opposition to gravity.
Mrs. B. And yet it is a consequence of their
pressure downwards. When, for example, you pour
water into a tea-pot, the water rises in the spout to
a level with the water in the pot. The particles of
water at the bottom of the pot are pressed upon by
the particles above them ; to this pressure they will
yield, if there is any mode of making way for th©
superior particles, and as they cannot descend, they
will change their direction and rise in the spout.
Suppose the tea-pot to be filled with columns of par-
ticles of water similar to that described in fig. 4. the
particle 1 at the bottom will be pressed laterally by
the particle 2, and by this pressure be forced into the
spout, where, meeting with the particle 3, it presses
it upwards, and this pressure will be continued, from
3 to 4, from 4 to 3, and so on, till the water in the
spout has risen to a level with that in the pot.
Emily, if it were not for this pressure upwards,
forcing the water to rise in the spout, the equilibrium
of the fluid would be destroyed.
Caroline. True ; but then the tea-pot is wide and
large, and the weight of so great a body of water as
the pot will contain, may easily force up and support
so small a quantity as will fill the spout. But would
the same effect be produced if the spout and the pot
were of equal dimensions ?
Mrs. B. Undoubtedly it would. You may even
reverse the experiment by pouring water into the
spout, and you will find that the water will rise in the
pot to a level with that in the spout ; for the pressure
of the small quantity of water in the spout will force
up and support the larger quantity in the pot. In the
pressure upwards, as well as that laterally, you see
that the force of pressure depends entirely on the
height, and is quite independent of the horizontal
dimensions of the fluid.
As a tea-pot is not transparent, let us try the ex-
periment by filling this large glass goblet by means
of this narrow tube. (fig. 6.)
152 MECHANICAL PROPERTIES OF FLUIDS.
Caroline. Look, Emily, as Mrs. B. fills it, how the
water rises in the goblet, to maintain an equilibrium
with that in the tube.
Now, Mrs. B., will you let me fill the tube by pour-
ing water into the goblet ?
Mrs. B. That is impossible. However, you may
try the experiment, and I donbt not but that .you will
be able to account for its failure.
Caroline. It is very sins^ular, that if so small a
column of water as is contaim^d in the tube can force
up and support the whole contents of the goblet, that
the weight of all the w iter in the goblet should not
be able to force up the small quantity required to fill
the tube : — oh, I see now the reason, water in the
goblet cannot force that in the tube above its level,
and as the end of the tube is considerably higher than
the goblet, it can never be filled by pouring water in-
to the goblet.
Airs. B. And if you continue to pour water into
the goblet when it is full, the water will run over in-
stead of rising above the level in the tube.
I shall now explain to you the meaning of the spe-
cific grarity of bodies.
Caroline. What ! is there another species of gravi-
ty with which we are not yet acquainted ?
Airs. B. No ; the specific gravity of a body means
simply its weight compared with that of another
body of the same size. When we say, that substances
such as lead and stones are heavy, and that others,
such as paper and feathers, are light, we speak compara-
tively ; that is to say, that the first are heavy, and the
latter light in comparison with the generality of sub-
stances in nature. Would you call wood and chalk
light or heavy bodies ?
Caroline, Some kinds of wood are heavy certain-
ly, as oak and mahogany ; others are light, as deal
and box.
Emily. I think I should call wood in general a
heavy body, for deal and box are light only in com-
parison to wood of a heavier description. I am at a
MECHANICAL PROPERTIES OP FLUIDS. 153
loss to determine whether chalk should be ranked as
a heavy or a light body; I should be inclined to say the
former, if it was not that it is lighter than most other
minerals. I perceive, that we have but vague notions
of light and heavy. I wish there was some standard
of comparison, to which we could refer the weight
of all other bodies.
A/rs. B. The necessity of such a standard has been
so much felt, that a body has been fixed upon for this
purpose. What substance do you think would be
best calculated to answer this end ?
Caroline, It must be one generally known and
easily obtained, lead or iron, for instance.
Mrs. B. All the metals expand by heat, and con-
dense by cold. A piece of lead, let us say a cubic
inch for instance, would have less specific gravity in
summer than in winter ; for it would be more dense
in the latter season.
Caroline. But, Mrs. B., if you compare the weight
of equal quantities of difforcnt bodies, they vv ill all
be alike. You know the old saying, that a pound of
feathers is as heavy as a pound of lead ?
Mrs. B. When therefore we compare the weight
of different kinds of bodies, it would he absurd to take
quantities of equal weight, we must take quantities of
equal bulk; pints or quarts, not ounces or pounds.
Caroline. Very true ; I perplexed myself by think-
ing that quantity referred to weight, rather than to
measure. It is true, it would be as absurd to com-
pare bodies of the same size in order to ascertain
which was largest, as to compare bodies of the same
weight in order to discover which was heaviest.
Mrs. B. In estimating the specific gravity of bo-
dies, therefore, we must compare equal bulks, and
we shall find that their specific gravity will be pro-
portional to their weights. The body which has
been adopted as a standard of reference is distilled
water.
Emily. I am surprised that a fluid should have
been chosen for this purpose, as it must necessarily
154 MECHANICAL PROPERTIES OF FLUIDS.
be contained in some vessel, and the weight of the
vessel will require to be deducted.
Mrs. B. In order to learn the specific gravity of
a solid body, it is not necessary to put a certain mea-
sure of it in one scale, and an equal measure of water
into the other scale ; but simply to weigh the body
under trial in water. If you weigh a piece of gold
in a glass of water, will not the gold displace just as
much water, as is equal to its own bulk.
Caroline. Certainly, where one body is, another
cannot be at the same time ; so that a sufficient
quantity of water must be removed, in order to make
way for the gold.
Mrs. B. Yes, a cubic inch of water to make room
for a cubic inch of gold ; remember that the bulk
alone is to be considered, the weight has nothing to
do with the quantity of water displaced, for an inch
of gold does not occupy more space, and therefore
will not displace more water than an inch of ivory,
or any other substance, that will sink in water^
Well, you will perhaps be surprised to hear that the
gold will weigh less in water, than it did out of it.
Emily. And for what reason ?
Mrs. B. On acronnt of the upward pressure of the
particles oi water, which in some measure supports
the gold, and, by so doing, diminishes its weight. If
the body immersed in water was of the same weight
as that fluid, it would be wholly supported by it,
just as the water which it displaces was supported
previous to its making way for the solid body. If
the body is heavier than the water, it cannot be
wholly supported by it ; but the water will offer
some resistance to its descent.
Caroline. And the resistance which water offers
to the descent of heavy bodies immersed in it, (since
it proceeds from the upward pressure of the parti-
cles of the fluid,) must in all cases, 1 suppose, be the
same ?
Mrs. B. Yes ; the resistance of the fluid is pro-
portioned to the bulk, and not to the weight of the
MECHANICAL PROPERTIES OP FLUIDS. 155
body immersed in it ; all bodies of the same size,
therefore, lose the same quantity of their weight in
water. Can you form any idea what this loss will
be?
Emily. I should think it would be equal to the
weii^ht of the water displaced ; for, since that por-
tion of the water was supported before the immer-
sion of the solid body, an equal weight of the solid
body will be supported.
Mrs. B. You are perfectly rioht ; a body weighed
in water loses just as much of its weit^ht, as is equal
to that of the water it displaces ; so that if you were
to put the water displaced into the scale to vvliich the
body is suspended, it would restore the balance.
You must observe, that when you weig;h a body
in water, in order to ascertain its sperilic gravity,
you must not sink the basin of the balance in the
water ; but either suspend the body to a hook at
the bottom of the basin, or else take off the basin,
and suspend it to the arm of the balance, (fii?. 7.)
Now suppose that a cubic inch of gold weighed 19
ounces out of water, and lost one ounce of its weight
by being weighed in water, what would be its spe-
citic gravity ?
Caroline. The cubic inch of water it displaced
must weigh that one ounce ; and as a cubic inch of
gold weighs 19 ounces, gold is 19 times as heavy ae
water.
Emily. I recollect having seen a table of the
comparative weights of bodies, in which gold appear-
ed to me to be estimated at 19 thousand times the
weight of water.
Mrs. B. You misunderstood the meaning of the
table. In the estimation you allude to, the weight of
water was reckoned at 1000. You must observe, that
the weight of a substance when not compared to that
of any other, is perfectly arbitrary ; and when water
is adopted as a standard, we may denominate its
weight by any number we please ; but then the
156 MECHANICAL PROPERTIES OF FLUIDS.
weight of all bodies tried by this standard must be
signified by proportional numbers.
Caroline, We may call the weii^ht of water, for
example, one, and then that of gold would be nine-
teen ; or if we chose to call the weight of water
1000, that of gold would be 19,000. In short, the
specific gravity means how much more a body weighs
than an equal bulk < f water.
Mrs. B. It is rather the weight of a body compa-
red with that of water ; for the specific gravity of
many substances is le»s than that of water.
Caroline. Then you cannot ascertain the specific
gravity of such substances in the same manner as that
of gold ; for a body that is lighter than water will
float on its surface without displacing any water.
Mrs. B. if a body were absolutely light, it is true
that it would not displace a drop of water, but the bo-
dies we are treating of have all some weight, hovve-
Ter small ; and will, therefore, displace some quanti-
ty of water. If the body be lighter than water, it
will not sink to a level with the surfiice of the water,
and therefore it will not displace so much water as is
equal to its bulk ; but it will displace as much as is
equal to its weight. A ship, you must have observed,
sinks to some depth in water, and the heavier it is la-
den the deeper it sinks, as it always displaces a quan-
tity of water equal to its weight.
Caroline. But you said just now, that in the immer-
sion of gold, the bulk, and not the weight of body,
was to be considered. ,
Mrs. B. That is the case with all substances
which are heavier than water ; but since those which
are lighter do not displace so much as their own bulk^
the quantity they displace is not a test of their speci-
fic gravity.
In order to obtain the specific gravity of a body
which is lighter than water, you must attach to it a
heavy one, whose specific gravity is known, and im-
merse them together ; the specific gravity of thp
lighter body may then be easily calculated.
MECHANICAL PROPERTIES OF i LUIJJa. 157
Emily. But are there not some bodies which have
Exactly the same specific gravity as water ?
Mrs. B. Undoubtedly ; and such bodies will re-
main at rest in whatever situation they are placed in
water. Here is a piece of wood which, by being im-
pregnated with a little sand, is rendered precisely of
the weight of an equal bulk of water; in whatever
part of this vessel of water you place it, you will
lind that it will remain stationary.
Caroline. 1 shall first put it at the bottom ; from
thence, of course, it cannot rise, because it is not
lighter than water. Now I shall place it in the mid-
dle of the vessel ; it neither rises nor sinks, because
it is neither lighter nor heavier than the water. Now
I will lay it on the surface of the water ; but there it
sinks a little — what is the reason of that, Mrs. B. ?
Mrs. B. Since it is not lighter than the water, it
cannot float upon its surface ; since it is not heavier
than water, it cannot sink below its surface: it will
sink, therefore, only till the upper surface of both bo-
dies are on a level, so that the piece of wood is just
covered with water. If you poured a few drops of
water into the vessel, (so gently as not to increase
their momentum by giving them velocity,) they would
mix with the water at the surface, and not sink lower.
Caroline. This must, no doubt, be the reason
^vhy, in drawing up a bucket of water out of a well,
the bucket feels so much heavier when it rises above
the surface of the water in the well«5 for whilst you
raise it in the water, the water within the bucket be-
ing of the same specific gravity as the water on the
outside, will be wholly supported by the upward pres-
sure of the water beneath the bucket, and conse-
quently very little force will be required to raise it ;
but as soon as the bucket rises to the surface of the
well, you immediately perceive the increase of
weight.
Emily. And how do you ascertain the specific
gravity of fluids ?
Mrs. B. By means of an instrument called a hv-
14
158 MECHANICAL PROPERTIES OF FLUIDS.
drometer, which I will show you. It consists of a
thin glass ball, A, (fig. 8. Plate XIII.) with a gradua-
ted tube, B, and the specific gravity of the liquid is es-
timated by the depth to which the instrument sinks in
it. There is a smaller ball, C, attached to the in-
strument below, which contains a little mercury ; but
this is merely for the purpose of equipoising the in-
strument, that it may remain upright in the liquid un-
der trial.
I must now take leave of you ; but there remain
yet many observations to be made on fluids : we
shall, therefore, resume this subject at our next inter-
view.
CONVERSATION XI.
OF SPRINGS, FOUNTAINS, &c.
Of the Ascent of Vapour mid the Formation of Clouds.
~ Of the Formation and Fall of Rain, <^c. — Of the
Formation of Springs. — Of Rivers and Lakes. — Of
Fountains.
CAROLINE. There is a question I am very de-
sirous of asking you respecting fluids, Mrs. B., which
has often perplexed me. What is the reason that the
great quantity of rain which falls upon the earth and
sinks into it, does not, in the course of time, injure its
solidity ? The sun and the wind, I know, dry the sur-
face, but they have no effect on the interior parts,
where there must be a prodigious accumulation of
moisture.
Mrs. B. Do you not know that, in the course of
time, all the water which sinks into the ground rises
out of it again ? It is the same water which succes-
sively forms seas, rivers, springs, clouds, rain, and
sometimes hail, snow, and ice. If you will take the
trouble of following it through these various changes,
you will understand why the earth is not yet drowned
by the quantity of water which has fallen upon it
since its creation ; and you will even be convinced,
that it does not contain a single drop more water
now than it did at that period.
Let us consider how the clouds were originally
formed. When the first rays of the sun warmed the
surface of the earth, the heat, by separating the par-
ticles of water, rendered them lighter than the air.
160 ON SPRINGS, FOUNTAINS, &C.
This, you know, is the case with steam or vapour.
What then ensues ?
Caroline. When lighter than the air it will natu-
rally rise ; and now I recollect your telling us in a
preceding lesson, that the heat of the sun transform-
ed the particles of water into vapour, in consequence
of which it ascended into the atmosphere, where it
formed clouds.
Mrs. B. We have then already followed water
through two of its transformations : from water it her
comes vapour, and from vapour clouds.
Emily. But since this watery vapour is lighter
than the air, why does it not continue to rise ; and
why does it unite again to form clouds ?
Mrs. B. Because the atmosphere diminishes in
density, as it is more distant from the earth. The
vapour, therefore, which the sun causes to exhale,
not only from seas, rivers, and lakes, but likewise
from the moisture on the land, rises till it reaches a
region of air of its own specific gravity ; and there,
you know, it will remain stationary. By the fre-
quent accession of fresh vapour it gradually accumu-
lates, so as to form those large bodies of vapour,
which we call clouds ; and these, at length, becom-
ing too heavy for the air to support, they fall to the
ground.
Caroline. They do fall to the ground, certainly,
when it rains ; but, according to your theory, I should
have imagined, that when the clouds became too hea-
vy for the region of air in which they were situated
to support them, they would descend till they reach-
ed a stratum of air of their own weight, and not fall to
the earth ; for as clouds are formed of vapour, they
cannot be so heavy as the lowest regions of the at-
mosphere, otherwise the vapour would not have risen.
Mrs. B. If you examine the manner in which the
clouds descend, it will obviate tliis objection. In fall-
ing, several of the watery particles come within the
sphere of each otlier's attraction, and unite in the
form of a drop of water. The vapour, thus tran?-
ON SPRINGS, F0CNTAINS,&C. 161
formed into a shower, is heavier than any part of the
atmosphere, and consequently descends to the earth.
Caroline. How wonderfully curious I
Mrs. B. It is impossible to consider any part of
nature attentively without being struck with admira-
tion at the wisdom it displays ; and I hope you will
never contemplate these wonders without feeling
your heart glow with admiration and gratitude to-
wards their bounteous Author. Observe, that if the
waters were never drawn out of the earth, all vege-
tation would be destroyed by the excess of moisture;
if, on the other hand, the plants were not nourished
and refreshed by occasional showers, the drought
would be equally fatal to them. If the clouds con-
stantly remained in a state of vapour, they might, as
you remarked, descend into a heavier stratum of the
atmosphere, but could never fall to the ground ; or
were the power of attraction more than sufficient to
convert the vapour into drops, it would transform the
cloud into a mass of water, which, instead of nourish-
ing, would destroy the produce of the earth.
Water then ascends in the form of vapour, and
descends in that of rain, snow, or hail, all of which
ultimately become water. Some of this falls into the
various bodies of water on the surface of the globe,
the remainder upon the land. Of the latter, part re-
ascends in the form of vapour, part is absorbed by
the roots of vegetables, and part descends into the
bowels of the earth, where it forms springs.
Emily. Is rain and spring-water then the same ?
Mrs. B. Yes, originally. The only difference
between rain and spring-water, consists in the foreign
particles which the latter meets with and dissolves in
its passage through the various soils it traverses.
Caroline. Yet spring water is more pleasant to
the taste, appears more transparent, and, I should
have supposed, would have been more pure than rain
water.
Mrs. B. No ; excepting distilled water, rain water
is the most pure we can obtain ; and it is its purity
14*
16:2 ON SPRINGS, FOUNTAINS, SzC,
which renders it insipid, whilst the various salts and
different ingredients, dissolved in spring water, give
it a species of flavour, without in any degree affecting
Its transparency : and the filtration it undergoes
through gravel and sand in the bowels of the earth,
cleanses it from all foreign matter which it has not
the power of dissolving.
When rain falls on the surface of the earth, it con-
tinues making its way downwards through the pores
and crevices in the ground. When several drops
meet in their subterraneous passage, they unite and
form a little rivulet ; this, in its progress, meets with
other rivulets of a similar description, and they pur-
sue their course together in the bowels of the earth,
till they are stopped by some substance which they
cannot penetrate.
Caroline. But you said that water could penetrate
even the pores of gold, and they cannot meet with a
substance more dense ?
Mrs. B. But water penetrates the pores of gold,
only when under a strong compressive force, as in
the Florentine experiment ; now, in its passage to-
wards the centre of the earth, it is acted upon by
no other power than gravity, which is not sufficient to
make it force its way even through a stratum of clay.
This species of earth, though not remarkably dense,
being of great tenacity, will not admit the particles
of water to pass. When water encounters any sub-
stance of this nature, therefore, its progress is stopped,
and the pressure of the accumulating waters forms a
bed, or reservoir. This will be more clearly explained
by fig. 9. Plate XIII. which represents a section, or
the interior of a hill or mountain. A, is a body of
water such I have described, which, when filled up
as high as B, (by the continual accession of waters it
receives from the ducts or rivulets a, a, a, a,) finds a
passage out of the cavity, and, impelled by gravity, it
runs on, till it makes its way out of the ground at the
fide of the hill, and there forms a spring, C.
Caroline, Gravity impels downwards towards the
©N SPRINGS, FOUNTAINS, &LC, 16,3
centre of the earth ; and the spring in this figure
runs in a horizontal direction.
Mrs. B. Not entirely. There is some declivity
from the reservoir to the spot where the water issue*
out of the ground : and gravity you know will bring
bodies down an inclined plane, as well as in a per-
pendicular direction.
Caroline. But though the spring may descend, on
first issuing, it must afterwards rise to reach the sur-
face of the earth ; and that is in direct opposition to
gravity.
Mrs. B. A spring can never rise above the level
of the reservoir whence it issues ; it must, therefore,
find a passage to some part of the surface of the
earth that is lower or nearer the centre than the re-
servoir. It is true that, in this figure, the spring
rises in its passage from B to C occasionally ; but
this, I think, with a little reflection, you will be able
to account for.
Emily. Oh, yes ; it is owing to the pressure of
fluids upwards, and the water rises in the duct upon
the same principle as it rises in the spout of a tea-pot ;
that is to say, in order to preserve an equilibrium
with the water in the reservoir. Now I think I un-
derstand the nature of springs : the water will flow
through a duct, whether ascending or descending,
provided it never rises higher than the reservoir.
Mrs. B. Water may thus be conveyed to every
part of a town, and to the upper part of the houses,
if it is originally brought from a height superior to
any to which it is conveyed. Have you never ob-
iserved, when the pavement of the streets has beea
mending, the pipes which serve as ducts for the con-
veyance of the water through the town ?
Emily. Yes, frequently ; and I have remarked
that when any of these pipes have been opened, the
water rushes upwards from them with great velocity,
which, I suppose, proceeds from the pressure of the
water in the reservoir, which forces it out.
164 ON SPRINGS, rOUNTAINS, Lc.
Caroline. I recollect having once seen a very cu-
rious glass, called Tantalus's cup ; it consists of a
goblet, containing a small figure of a man, and whate-
ver quantity of water you pour into the goblet, it ne-
ver rises higher than the breast of the figure. Do
you know how that is contrived ?
Mrs. B. It is by means of a syphon, or bent tube,
which is concealed in the body of the figure. It rises
through one of the legs as high as the breast, and
there turning descends through the other leg, and
from thence through the foot of the goblet, where the
water runs out. (fig. 1. Plate XIV.) When you
pour water into the glass A, it must rise in the sy-
phon B, in proportion as it rises in the glass ; and
when the glass is filled to a level with the upper part
of the syphon, the water will run out through the
other leg of the figure, and will continue running out,
as fast as you pour it in ; therefore the glass can ne-
ver fill any higher.
Emify. I think the new well that has been made
at our country-house, must be of that nature. We
had a great scarcity of water, and my father has been
at considerable expense to dig a well ; after penetrat-
ing to a great depth before water could be found, a
spring was at length discovered, but the water rose
only a few feet above the bottom of the well ; and
sometimes it is quite dry.
Mrs. B. This has, however, no analogy to Tanta-
lus's cup, but is owing to the very elevated situation
of your country-house.
Emily. I believe I guess the reason. There can-
not be a reservoir of water near the summit of a hill ;
as in such a situation, there will not be a sufficient
number of rivulets formed to supply one ; and with-
out a reservoir there can be no spring. In such si-
tuations, therefore, it is necessary to dig very deep,
in order to meet with a spring ; and when we give
it vent, it can rise only as high as the reservoir from
whence it flows, which will be but little, as the reser-
FLATE. xnr.
F^. 1.
%• ^•
F^. s
ON SPRINGS, FOUNl'AINS, &C. 166
voir must be situated at some considerable depth be-
low the summit of the hill.
Caroline. Your explanation appears very clear
and satisfactory ; but 1 can contradict it from experi-
ence. At the very top of a hill, near our country-
house, there is a large pond, and, according to your
theory, it would be impossible there should be springs
in such a situation to supply it with water. Then
you know that 1 have crossed the Alps, and I can as-
sure you, that there is a fine lake on the summit of
Mount Cenis, the highest mountain we passed over.
Mrs. B. Were there a lake on the summit of
Mount Blanc, which is the highest of the Alps, it
would indeed be wonderful. But that on Mount Ce-
nis is not at all contradictory to our theory of
springs ; for this mountain is surrounded by others,
much more elevated, and the springs which feed the
lake must descend from reservoirs of water formed in
those mountains. This must also be the case with the
pond on the top of the hill : there is doubtless some
more considerable hill in the neighbourhood, which
supplies it with water.
Emily. 1 comprehend perfectly why the water
in our well never rises high ; but 1 do not understand
why it should occasionally be dry.
Mrs. B. Because the reservoir from which it
flows, being in an elevated situation, is but scantily
supplied with water ; after a long drought, therefore,
it may be drained, and the spring dry, till the reser-
voir be replenished by fresh rains. It is not uncom-
mon to see springs flow with great violence in wet
weather, and at other times be perfectly dry.
Caroline. But there is a spring in our grounds
»vhich more frequently flows in dry than in wet wea-
ther : how is that to be accounted for ?
Mrs. B. The spring probably comes from a
reservoir at a great distance, and situated very deep
in the ground ; it is, therefore, some length of time
before the rain reaches the reservoir, and another
considerable portion must elapse, whilst the water is
166 ON SPRINGS, FOUNTAINS, &€.
making its way from the reservoir to the surface of
the earth ; so that the dry weather may probably
have succeeded the rains before the spring begins to
flow, and the reservoir may be exhausted by the time
the wet weather sets in again.
Caroline. I doubt not but this is the case, as the
spring is in a very levy situation, therefore the reser-
voir may be at a great distance from it.
Mrs. B. Springs which do not constantly flow, are
called intermitting, and are occasioned by the reser-
voir being imperfectly supplied. Independently of
the situation, this i^ always the case when the duct or
ducts which convey the water into the reservoir are
smaller than those which carry it off".
Caroline. If it runs out faster than it runs in, it will
of course sometimes be empty. And do not rivers al-
so derive their source from springs ?
Mrs. B. Yes, they generally take their source in
mountainous countries, where springs are most abun-
dant.
Caroline. I understood you that springs were
more rare in elevated situations.
Mrs. B. You do not consider that mountainous
countries abound equally with high and low situa-
tions. Reservoirs of water, which are formed in the
bosom of mountains, generally find a vent either on
their declivity, or in the valley beneath ; while sub-
terraneous reservoirs, formed in a plain, can seldom
find a passage to the surface of the earth, but remain
concealed, unless discovered by digging a well.
When a spring once issues at the surface of the earth
it continues its course externally, seeking always a
lower ground, for it can no longer rise.
Emily. Then what is the consequence, if the
spring, or I should now rather call it a rivulet, runs
into a situation which is surrounded by higher
ground.
Mrs. B. Its course is stopped, the water accumu-
lates, and it forms a pool, pond, or lake, according to
the dimensions of the body of water. The Lake of
6N SPRINGS, FOUNTAINS, &e» 165'
Geneva, in all probability, owes its origin to the
Rhone, which passes through it : if, when this river
first entered the valley, which now forms the bed of
the Lake, it found itself surrounded by higher
grounds, its waters would there accumulate, till they
rose to a level with that part of the valley where the
Rhone now continues its course beyond the Lake, and
from whence it flows through valleys, occasionally
forming other small lakes, till it reaches the sea.
Emily. And are not fountains of the nature of
springs ?
Airs. B. Exactly. A fountain is conducted per-
pendicularly upwards, by the spout or adjutage A,
through which it flows ; and it will rise nearly as
high as the reservoir B, from whence it proceeds,
(Plate XIV. tig. 2.)
Caroline. Why not quite as high ?
Mrs. B. Because it meets with resistance from
the air in its ascent ; and its motion is impeded by
friction against the spout, where it rushes out.
Emily. But if the t«ibe through which the water
rises be smooth, can there be any friction ? especial-
ly with a fluid, whose particles yield to the slightest
impression.
Airs. B. Friction (as we observed in a former
lesson) may be diminished by polishing, but can ne-
ver be entirely destroyed ; and though fluids are less
susceptible of friction than solid bodies, they are still
afiected by it. Another reason why a fountain will
not rise so high as its reservoir, is, that as all the par-
ticles of water spout from the tube with an equal ve-
locity, and as the pressure of the air upon the exte-
rior particles must diminish their velocity, they will
in some degree strike against the under parts, and
force them sideways, spreading the column into a
head, and rendering it both wider and shorter than it
otherwise would be.
At our next meeting, we shall examine the mecha-
nir'al properties of the air, which, being an elastic
fluid, differs in many respects from liquids.
CONVERSATION XH.
ON THE MECHANICAL PROPERTIES OF AIR.
Of the Spring or Elasticity of the Air. — Of the "weight
of the Air. — Experiments with the Air Pump. — Of
the Barometer. — Mode of weighing Air. — Specific
Gravity of Air. — Of Pumps. — Description of the
Sucking Pump. — Description of the Forcing Pump.
MRS. B. At our last meeting we examined the
properties of fluids in fijeneral, and more particularly
of such fluids as are called liquids.
There is another class of fluids, distinguished by
the name of aeriform or elastic fluids, the principal
of which is the air we breathe, which surrounds the
earth, and is called the atmosphere.
Emily. There are then other kinds of air besides
the atmosphere ?
Mrs. B. Yes, a great variety ; but they differ only
in their chemical, and not in their mechanical pro-
perties ; and as it is the latter we are to examine, we
shall not at present inquire into their composition, but
confme our attention to the mechanical properties of
elastic fluids in general.
Caroline. And from whence arises this difference ?
Mrs. B. There is no attraction of cohesion be-
tween the particles of elastic fluids ; so that the ex-
pansive power of heat has no adversary to contend
with but gravity ; any increase of temperature, there-
fore, expands elastic fluids prodigiously, and a dimi-
nution proportionally condenses them.
MECHANICAL PROPERTIES OP AIR. 16!^
The most essential point in which air differs from
other fluids, is .by its spring or elasticity ; that is to
say, its power of increasing or diminishing in bulk,
according as it i? more or less compressed : a power
of which I have mformed you liquids are almost
wholly deprived.
Emily. I think I understand the elasticity of the
air very well, from what you formerly said of it ;*
but wluit perplexes me is, its having gravity ; if it is
heavy, and we are surrounded by it, why do we not
feel its weight ?
Caroline. It must be impossible to be sensible of
the weight of such infinitely small particles, as those
of which the air is composed : particles which are
too small to be seen, must be too light to be felt.
Mrs. B. You are mistaken, my dear ; the air is
much heavier than you imagine ; it is true, that the
particles which compose it are small ; but then, re-
flect on their quantity : the atmosphere extends to
about the distance of 45 miles from the earth, and its
gravity is such, that a man of middling stature is com-
puted (when the air is heaviest) to sustain the weight
of about 14 tons.
Caroline. Is it possible ! I should have thought
such a weight would have crushed any one to atoms.
Mrs. B. That would, indeed, be the case, if it
were not for the equality of the pressure on every
part of the body; but, when thus diffused, we can
bear even a much greater weight, without any consi-
derable inconvenience. In bathing we support the
weight and pressure of the water, in addition to that
of the atmosphere ; but because this pressure is
equally distributed over the body, we are scarcely
sensible of it ; whilst if your shoulders, your head,
or any particular part of your frame were loaded
with the additional weight of a hundred pounds, you
■would soon sink under the fatigue. Besides this, our
See page 37-
170 MECHANICAL PROPERTIEa OP AIR.
bodies contain air, the spring of which counterbalan-
ces the weight of the external air, and renders us less
sensible of its pressure.
Caroline. But if it were possible to relieve me
from the weight of the atmosphere, should I not feel
more light and agile ?
Mrs. B. On the contrary, the air within you
meeting with no external pressure to restrain its elas-
ticity, would distend your body, and at length, burst-
ing the parts which confined it, put a period to your
existence.
Caroline. This weight of the atmosphere, then,
which I was so apprehensive would crush me, is, in
reality, essential to my preservation.
Emily. J once saw a person cupped, and was told
that the swelling of the part under the cup was produ-
ced by taking away from that part the pressure of the
atmosphere ; but 1 could not understand how this
pressure produced such an effect.
JUrs. B. The air pump affords us the means of
making a great variety of interesting experiments on
the weight and pressure of the air : some of them
you have already seen. Do you not recollect, that in
a vacuum produced within the air-pump, substances
of various weights fell to the bottom in the same
time ; why does not this happen in tlie atmosphere ?
Caroline. I remember you told us it was owing to
the resistance which light bodies meet with from the
air during their fall.
Mrs. B. Or, in other words, to the support which
they received from the air, and which prolonged the
time of their fall. Now, if the air were destitute of
weight, how could it support other bodies, or retard
their fall ?
I shall now show you some other experiments,
which illustrate, in a striking manner, both the
weight and elasticity of air. 1 shall tie a piece of
bladder over this glass receiver, which, you will ob-
serve, is open both at the top as well as below.
Caroline, Why do you wet the bladder first ?
MECHANICAL PROPERTIES OF AIR. 171
Mrs, B. It expands by wetting, and contracts in
drying ; it is also more soft and pliable when wet, so
that I can make it tit better, and when dry it will be
tighter. We must hold it to the fire in order to dry ;
but not too near, least it should burst by sudden con-
traction. Let us now fix it on the air-pump and ex-
haust the air from underneath it — you will not be
alarmed if you hear a noise ?
Eniihf. It was as loud as the report of a gun, and
the bladder is burst ! Pray explain how the air is con-
cerned in this experiment.
Mrs. B. It is the effect of the weight of the at-
mosphere on the upper surface of the bladder, when
I had taken away the air from the under surface ; so
that there was no longer any reaction to counterba-
lance the pressure of the atmosphere on the receiver.
You observed how the bladder was pressed inwards
by Ihe weight of the external air, in proportion as I
exhausted the receiver : and before a complete va-
cuum was formed, the bladder, unable to sustain the
violence of the pressure, burst with the explosion
you have just heard.
I shall now show you an experiment, which proves
the expansion of the air, contained within a body
when it is relieved from the pressure of the external
air. You would not imagine that there was any air
contained within this shrivelled apple, by its appear-
ance ; but take notice of it when placed within a re-
ceiver, from which 1 shall exhaust the air.
Caroline. How strange ! it grows quite plump,
and looks like a fresh-gathered apple.
Mrs. B. But as soon as I let the air again into the
receiver, the apple you see returns to its shrivelled
state. When 1 took away the pressure of the atmos-
phere, the air within the apple expanded and swell-
ed it out ; but the instant the atmospherical air was
restored, the expansion of the internal air was check-
ed and repressed, and the apple shrunk to its former
dimensions.
You may make a similar experiment with this lit-
172 MECHANICAL PROPERTIL OF AIR.
tie bladder, which you see is perfectly flaccid, an^
appears to contain no air : in this state, i shall tie up
the neck of the bladder, so that whatever air remains
within it may not escape, and then place it under the
receiver. Now observe, as I exhaust the receiver,
iiow the bladder distends ; this proceeds from the
great dilatation of the small quantity of air which was
enclosed within the bladder when 1 tied it up ; but as
soon as I let the air into the receiver, that which the
hladder contains condenses, and shrinks into its small
©ompass within the folds of the bladder.
Emily. These experiments are extremely amU'
sing, and they afl'ord clear proofs both of the weight
and elasticity of the air; but I should like to know
exactly how much the air weighs.
Mrs. B. A column of air reaching to the top of the
atmosphere, and whose base is a square inch, wej^hs
15 lbs. when the air is heaviest; therefore every
square inch of our bodies sustains a weight of 15 lbs. :
and if you wish to know the weight of the whole of
the atmosphere, you must reckon how many square
inches there are on the surface of the globe, and
multiply them by 15.
Emily. But are there no means of ascertaining,
the weight of a small quantity of air 1
Mrs. B. Nothing more easy. I shall exhaust the
air from this little bottle by means of the air-pump ;
and having emptied the bottle of air, or, in other
words, produced a vacuum within it, I secure it by-
turning this screw adapted to its neck : we may now
find the exact weight of this bottle, by putting it into
one of the scales of a balance. Jt weighs you see
just two ounces ; but when 1 turn the screw, so as to
admit the air into the bottle, the scale which contains
it preponderates.
Caroline. No doubt the bottle filled with air is
heavier than the bottle void of air ; and the addition-
al weight required to bring the scales again to a ba-
lance, must be exactly that of the air which the bot-
tle now contains^
MECHANICAL PROPERTIES OF AIR. 173
Mrs. B. That weight, you see, is almost two
grains. The dimensions of this bottle are six cubic
inches. Six cubic inches of air, therefore, at the
temperature of this room, weighs nearly 2 grains.
Caroline. Why do you observe the temperature
of the room, in estimating the weight of the air.
Mrs. B. Because heat rarefies air, and renders it
lighter ; therefore the warmer the air is which you
weigh, the lighter it will be.
If you should now be desirous of knowing the spe-
cific gravity of this air, we need only fill the same
bottle with water, and thus obtain the weight of an
equal quantity of water — which you see is 1515 grs. j
now by comparing the weight of water to that of air,
we find it to be in the proportion of about 800 to 1.
1 will show you another instance of the weight of
the atmosphere, which I think will please you : you
know what a barometer is ?
Caroline. It is an instrument which indicates the
state of the weather, by means of a tube of quicksil-
ver ; but how, I cannot exactly say.
Mrs. B. It is by showing the weight of the atmos-
phere. The barometer is an instrument extremely
simple in its construction : in order that you may un-
derstand it, I will show you how it is made I first
fill a glass tube A B, (fig. 3. Plate XIV.) about three
feet in length, and open only at one end, with mercu-
ry ; then stopping the open end with my finger, I im-
merse it in a cup C, containing a little mercury.
Emily. Part of the mercury which was in the
tube, I observe, runs down into the cup ; but why
does not the whole of it subside in the cup, for it is
contrary to the law of the equilibrium of fluids, that
the mercury in the tube should not descend to a level
with that in the cup ?
Mrs. B. The mercury that has fallen from the
tube into the cup, has left a vacant space in the up-
per part of the tube, to which the air cannot a,ain ac-
cess ; this space is therefore a perfect vacuum ; and
consequently the mercury in the tube is relieved
15*
174 MECHANICAL PROPERTIES OF AIK.
from the pressure of the atmosphere, whilst that m
the cup remains exposed to it.
Caroline. Oh, now I understand it ; the pressure
of the air on the mercury in the cup forces it to rise
in the tube, where it sustains no pressure.
Emily. Or rather supports the mercury in the
tube, and prevents it from faUing.
Mrs. B. That comes to the same thing ; for the
power that can support mercury in a vacuum, would
also make it ascend when it met with a vacuum.
Thus you see, that the equilibrium of the mercu-
ry is destroyed only to preserve the general equili-
brium of fluids.
Caroline. But this simple apparatus is, in appear-
ance, very unlike a barometer.
Mrs. B. It is all that is essential to a barometer.
The tube and the cup or vase are fixed on a board,
for the convenience of suspending it ; the board is
graduated for the purpose of ascertaining the height
at which the mercury stands in the tube ; and the
small moveable metal plate serves to show that
height with greater accuracy.
Emilij. And at what height will the weight of the
atmosphere sustain the mercury ?
Mrs. B. About 28 inches, as you will see by this
barometer ; but it depends upon the weight of the
atmosphere, which varies much according to the state
of the weather. The greater the pressure of the
air on the mercury in the cup, the higher it will as-^
cend in the tube. Now can yon tell me whether the
air is heavier in wet or dry weather.
Caroline. Without a moment's reflection, the air
roust be heaviest in wet weather. It is so depress-
ing, and makes one feel so heavy ; while in fine
weather I feel as light as a feather, and as brisk as
a bee.
Mrs. B. Would it not have been better to have
answered with a moment's reflection, Caroline ? It
wonld have convinced you, that the air must be hea^
yrest in dry weather, for it is then that the mercurv
MECHANICAL 1»R0PERTIES OP AIR. 17a
i3 tbund to rise in the tube, and consequently the
mercury in the cup must be most pressed by the air :
and yow know, that we estimate tlie dryness and fair-
ness of the weather by the height of the mercury in
the barometer.
Caroline. Why then does the air feel so heavy in
bad weather.
Mrs. B. Because it is less salubrious when im-
pregnated with damp. The lungs under these cir-
cumstances do not play so freely, nor does the blood
circulate so well : thus obstructions are frequently
occasioned in the smaller vessels, from which arise
colds, asthmas, agues, fevers, &:c.
Emily. Since the atmosphere diminishes in densi-
ty in the upper regions, is not the air more rare upon
a hill than in a plain ; and does the barometer indi-
cate this difference ?
Mrs. B. Certainly. The hills in this country are
not sufficiently elevated to produce any very conside-
rable effect on the barometer ; but this instrument is
so exact in its indications, that it is used for the pur-
pose of measuring the height of mountains, and of es-
timating the elevation of balloons.
Emily. And is no inconvenience experienced from
the thinness of the air in such elevated situations ?
Mrs. B. Oh, yes ; frequently. It is sometimes
oppressive, from being insufficient for respiration ;
and the expansion which takes place in the more
dense air contained within the body is often painful ;
it occasions distension, and sometimes causes the
bursting of the smaller blood-vessels in the nose and
ears. Besides, in such situations, you are more ex-
posed both to heat and cold ; for though the atmos-
phere is itself transparent, its lower regions abound
with vapours and exhalations from the earth, which
float in it, and act in some degree as a covering,
which preserves us equally from the intensity of the
sun's rays, and from the severity of the cold.
Caroline. Pray, Mrs. B., is not the thermometer
(Jonstrqcted on the same principles as the barometer ?
176 MECHANICAL PROPERTIES OF AIR.
Mrs. B. Not at all. The rise and fall of the fluid
in the thermometer is occasioned by the expansive
power of heat, and the condensation produced by
cold : the air has no access to it. An explanation of
it would, therefore, be irrelevant to our present sub-
ject.
Emily. I have been reflecting, that since it is the
weight of the atmosphere which supports the mercu-
ry in the tube of a barometer, it would support a co-
lumn of any other fluid in the same manner.
Mrs. B. Certainly ; but as mercury is heavier
than all other fluids, it will support a higher column
of any other fluid ; for two fluids are in equilibrium,
*vhen their height varies inversely as their densities.
We find the weight of the atmosphere is equal to sus-
taining a column of water, for instance, of no less than
32 feet above its level.
Caroline. The weight of the atmosphere is, then,
as great as that of a body of water the depth of 32 feet ?
Mrs. B. Precisely ; for a column of air of the
height of the atmosphere is equal to a column of wa-
ter of 32 feet, or one of mercury of 28 inches.
The common pump is constructed on this princi-
ple. By the act of pumping, the pressure of the at-
mosphere is taken off" the water, which, in conse-
quence, rises.
The body of a pump consists of a large tube or
pipe, whose lower end is immersed in the water
which it is designed to raise. A kind of stopper, call-
ed a piston, is fitted to this tube, and is made to slide
up and down it, by means of a metallic rod fastened t©
the centre of the piston.
Emily. Is it not similar to the syringe, or squirt,
with which you first draw in, and then force out wa-
ter ?
Mrs. B. It is ; but you know that we do not wish
to force the water out of the pump, at the same end
of the pipe at which we draw it in. The intention of
a pump is to raise water from a spring or well ; the
MECHANICAL PROPERTIES OP AIR. 177
pipe is, therefore, placed perpendicularly over the
water, which enters it at the lower extremity, and it
issues at a horizontal spout towards the upper part of
the pump. The pump, therefore, is rather a more
complicated piece of machinery than the syringe.
^ Its various parts are delineated in this tigure :
(fi^. 4. Plate XIV.) A B is the pipe or hody of the
pump, P the piston, V a valve, or little door in the
piston, which, opening upwards, admits the water to
rise through it, but prevents its returning, and Y a
similar valve in the body of the pump.
When the pump is in a state of inaction, the two
valves are closed by their own weight ; but when,
by drawing down the handle of the pump, the piston
ascends, it raises a column of air which rested upon it,
and produces a vacuum between the piston and the
lower valve Y, the air beneath this valve, which is
immediately over the surface of the water, conse-
quently expands, and forces its way through it ; the
water, then, relieved from the pressure of the air, as-
cends into the pump. A few strokes of the handle
totally excludes the air from the body of the pump»
and fills it with water, which, having passed through
both the valves, runs out at the spout.
Caroline. I understand this perfectly. When the
piston is elevated, the air and the water successively
rise in the pump ; for the same reason as the mercu-
ry rises in the barometer.
Emily. I thought that water was drawn up into a
pump, by suction, in the same manner as water may
be sucked through a straw.
Airs. B. It is so, into the body of the pump ; for
the power of suction is no other than that of produ-
cing a vacuum over one part of the liquid, into which
vacuum the liquid is forced by the pressure of the at- "^
mosphere on another part. The action of sucking
througli a straw consists in drawing in and conhning^
the breath, so as to produce a vacuum in the mouth ;
in consequence of which, the air within the straw
rushes into the mouth, and is followed by the. liquid.
178 MECHANICAL PROPERTIES OF AIR.
into which the lower end of the straw is immersed.
The principle, you see, is the same ; and the only
difference consists in the mode of producing a vacuum.
In suction, the muscular powers answer the purpose
of the piston and valves.
Emily. Water cannot, then, be raised by a pump
above 32 feet; for the pressure of the atmosphere
will not sustain a column of water above that height.
Mrs. B. 1 beg your pardon. It is true that there
must never be so ii;reat a distance as 32 feet from the
level of the water in the well, to the valve in the pis-
ton, otherwise the water would not rise through that
valve ; but when once the water has passed that open-
ing, it is no longer the pressure of air on the reservoir
which makes it ascend ; it is raised by lifting it up, as
you would raise it in a bucket, of which the piston
formed the bottom. This common pump is, there-
fore, called the sucking, or lifting-pump, as it is con-
structed on both these principles. There is another
sort of pump, called the forcing-pump : it consists of
a forcing power added to the sucking part of the pump.
This additional power is exactly on the principle of
the syringe : by raising the piston you draw the water
into the pump, and by descending it you force the wa-
ter out.
Caroline. But the water must be forced out at the
upper part of the pump ; and I cannot conceive how
that can be done by descending the piston.
Mrs. B. Figure 6. PI. XIV. will explain the diffi-
culty. The large pipe A B represents the sucking
part of the pump, which differs from the lifting-pump
only in its piston P being unfurnished with a valve, in
consequence of which the water cannot rise above it.
When, therefore, the piston descends, it shuts the
valve Y, and forces the water (which has no other
vent) into the pipe D : this is likewise furnished with
a valve V, which, opening outwards, admits the wa-
ter, but prevents its return.
The water is thus first raised in the pump, and then
forced into the pipe, by the alternate ascending and
MECHANICAL PROPERTIES OF AIR, 179
descendini; motion of the piston, after a few strokes
of the handle to till the pipe, from whence the water
i.- s at the spout.
h is now time to conclude our lesson. When
next we meet, 1 shall give you some account of wind,
and of sound, which will terminate our observations
on elastic fluids.
Caroline. And I shall run into the garden, to have
the pleasure of pumping, now that 1 understand the
construction of a pump.
Mrs. B. And, to-morrow, I hope you will be able
to tell me, whether it is a forcing or a common lifting
pump.
CONVERSATION XIII.
ON WIND AND SOUND.
Of Wind in General.— Of the Trade Wind.— Of the
Perwdical Trade Winds. — Of the Aerial Tides. —
Of Sound in General. — Of Sonorous Bodies. — Of
Musical Sounds. — Of Concord or Harmony, and
Melody.
MRS. B. Well, Caroline, have you ascertained
what kind of pump you have in yourj^arden ?
Caroline. 1 think it must be merely a lifting-
pump, because no more force is required to raise the
handle than is necessary to lift its weight : and in a
forcing-pump, by raising the handle, you force the
water into the smaller pipe, and the resistance the
water offers must require an exertion of strength to
overcome it.
Mrs. B. I make no doubt you are right ; for lift-
ing pumps, being simple in their construction, are by
far the most common.
1 have promised to day to give you some account
of the nature of wind. Wind is nothing more than
the motion of a stream or current of air, generally
produced by a partial change of temperature in the
atmosphere ; for when any one part is more heated
than the rest, that part is rarefied ; the equilibrium is
destroyed, and the air in consequence rises. When
this happens, there necessarily follows a motion of the
surrounding air towards that part, in order to re-
store it ; this spot, therefore, receives winds from
t>N WIND AND SOUND. 18l
every quarter. Those who live to the north of it ex-
perience a north wind ; those to the south, a south
wind ; — do you comprehend this ?
Caroline Perfectly. But what sort of weather
must those people have, who live on the spot where
ihese winds meet and interfere ?
Mrs. B. They have turbulent and boisterous
weather, whirlwinds, hurricanes, rain, lightning,
thunder, &c. This stormy weather occurs most fre-
quently in the torrid zone, where the heat is greatest :
the air being more rarefied there than m any other
part of the ^lobe, is lighter, and consequently ascends ',
whilst the air about the polar regions is continually
flowing from the poles, to restore the equilibrium.
Caroline. This motion of the air would produce a
regular and constant north wind to the inhabitants of
the northern hemisphere ; and a south wind to those
of the southern hemisphere, and continual storms at
the equator, where these two adverse winds would
meet.
Mrs. B. These winds do not meet, for they each
change their direction before they reach the equator.
The sun, in moving over the equatorial regions from
east to west, rarefies the air as it passes, and causes
the denser eastern air to flow westwards, in order to
restore the equilibrium ; thus producing a regular
east wind about the equator.
Caroline. The air from the west, then, constantly
goes to meet the sun, and repair the disturbance
which his beams have produced in the equilibrium of
the atmosphere. But 1 wonder how you will recon-
cile these various winds, Mrs. B. : you first led me
to suppose there was a constant struggle between op-
posite winds at the equator, producing storm and
tempest ; but now 1 hear of one regular invariable
wind, which must naturally be attended by calm
weather.
Emily. I think I comprehend it : do not these
winds from the north and south combine with the
16
182 ON WIND AND SOUND.
easterly wind about the equator, and form what are
called the trade-winds ?
Mrs. B. Just so, my dear. The composition of
the two winds nortli and east, produces a constant
north-east wind ; and that of the two winds south and
east, produces a regular south-east wind : these winds
extend to about thirty degrees on each side of the
equator, the regions further distant from it expe-
riencing only their respective north and south winds.
Caroline. But, Mrs. B., if the air is constantly
flowing from the poles to the torrid zone, there must
be a deficiency of air in the polar regions ?
Mrs. B. The light air about the equator, which ex-
pands and rises into the upper regions of the atmos-
phere, ultimately flows from thence back to the poles
to restore the equilibrium : if it were not for this re-
source, the polar atmospheric regions would soon be
exhausted by the stream of air, which, in the lower
strata of the atmosphere, they are constantly sending
towards the equator.
Carolitie. There is then a sort of circulation of
air in the atmosphere ; the air in the lower strata
flowing from the poles towards the equator, and in
the upper strata, flowing back from the equator to-
wards the poles.
Mrs. B. Exactly : I can show you an example of
this circulation on a small scale. The air of this
room being more rarefied than the external air, a
wind or current of air is pouring in from the crevices
of the windows and doors, to restore the equilibrium ;
but the light air with which the room is filled must
find some vent, in order to make way for the heavy
air which enters. If you set the door a-jar, and hold
a candle near the upper part of it, you will find that
the flame will be blown outwards, showing that there
is a current of air flowing out from the upper part of
the room. — Now place the candle on the floor close
by the door, and you will perceive, by the inclination
of the flame, that there is also a current of air setting
into the room.
ON WIND AND SOUND. 183
Caroline. It is just so ; the upper current is the
warm light air, which is driven out to make way for
the stream of cold dense air which enters the room
lower down.
Emily. I have heard, Mrs. B., that the periodical
winds are not so regular on land as at sea : what is the
reason of that ?
Mrs. B. The land reflects into the atmosphere a
much greater quantity of the sun's rays than the wa-
ter ; therefore, that part of the atmosphere which is
over the land, is more heated and rarefied than that
which is over the sea : this occasions the wind to set
in upon the land, as we find that it regularly does on
the coast of Guinea, and other countries in the torrid
zone.
Emily. I have heard much of the violent tempests
occasioned by the breaking up of the monsoons ; are
not they also regular trade-winds ?
Mrs. B. They are called periodical trade-winds,
as they change their course every half year. This
variation is produced by the earth's annual course
round the sun, when the north pole is inclined towards
that luminary one half of the year, the south pole
the other half. During the summer of the northern
hemisphere, the countries of Arabia, Persia, India
and China, are much heated, and reflect great quan-
tities of the sun's rays into the atmosphere, by which
it becomes extremely rarefied, and the equilibrium
consequently destroyed. In order to restore it, the
air from the equatorial southern regions, where it is
colder, (as well as from the colder northern parts,)
must necessarily have a motion towards those parts.
The current of air from the equatorial regions pro-
duces the trade-winds for the first six months, in all
the seas between the heated continent of Asia, and the
equator. The other six months, when it is summer
in the southern hemisphere, the ocean and countries
towards the southern tropic are most heated, and the
air over those parts most rarefied : then the air about
it84 ON WIND AND SOUND.
flhe equator alters iis course, and flows exactly in an
•pposite direction.
Caroline. This explanation of the monsoons is very
ourious ; but what does their breaking up mean ?
Mrs, B. It is the name given by sailors to the
shifting of the periodical winds ; they do not change
their course suddenly, but by degrees, as the sun
moves from one hemisphere to the other : this change
is usually attended by storms and hurricanes, very
dana^erous for shipping ; so that those seas are sel-
dom navigated at the season of the equinox.
Etniiy. 1 think I understand the winds in the tor-
rid zone perfectly well ; but what is it that occasions
the great variety of winds which occur in the tempe-
rate zones ? for, according to your theory, there
should be only north and south winds in those cli-
mates.
Mrs. B. Since so large a portion of the atmos-
phere as is over the torrid zone is in continued agi-
tation, these agitations in an elastic fluid, which yields
to the slightest impression, must extend every way to
a great distance ; the air, therefore, in all climates,
will suff"er more or less perturbation, according to the
situation of the country, the position of mountains, val-
leys, and a variety of other causes : hence it is easy
to conceive, that almost every climate must be liable
to variable winds.
On the seashore, there is almost always a gentle
sea-breeze setting in on the land on a summer's even-
ing, to restore the equilibrium which has been dis-
turbed by reflections from the heated surHice of the
shore during the day ; and when night has cooled the
land, and condensed the air, we generally find it, to-
wards morning, flowing back towards the sea.
Caroline. I have observed, that the wind, which-
ever way it blows, almost always falls about sunset ?
Mrs. B. Because the rarefaction of air in the par-
ticular spot which produces the wind, diminishes as
the sun declines, and consequently the velocity of the
wind abates.
ON WIND AND SOUND* 1 8^
Emily. Since the air is a gravitating fluid, is it not
affected by the attraction of the moon and the sun, ia
the same manner as the waters ?
Mrs. B. Undoubtedly ; but the aerial tides are as
much greater than those of water, as the density of
water exceeds that of air, which, as you may recol-
lect, we found to be about 800 to 1.
Caroline. What a prodigious protuberance that
must occasion! How much the weight of such a co-
lumn of air must raise the mercury in the barometer?
Emily. As this enormous tide of air is drawn up
and supported, as it were, by the moon, its weight
and pressure, I should suppose, would be rather di-
minished than increased ?
Mrs. B. The weight of the atmosphere is neither
increased nor diminished by the aerial tides. The
moon's attraction augments the bulk as much as it di-
minishes the weight of the column of air ; these ef-
fects, therefore, counterbalancing each other, the
aerial tides do not affect the barometer.
Caroline. I do not quite understand that.
Mrs. B. Let us suppose that the additional bulk of
air at high tide raises the barometer one inch ; and on
the other hand, that the support which the moon's
attraction affords the air diminishes its weight or pres-
sure, so as to occasion the mercury to fall one inch ;
under these circumstances the mercury must remain
stationary. Thus you see, that we can never be sen-
sible of aerial tides by the barometer, on account of
the equality of pressure of the atmosphere, whatever
be its height.
The existence of aerial tides is not, however, hy-
pothetical ; it is proved by the effect they produce on
the apparent position of the heavenly bodies ; but this
I cannot explain to you, till you understand the pro-
perties of light.
Emily. And when shall we learn them ?
Mr. . B. 1 shall first explain to you the nature of
sound, which is intimately connected with that of airj
16*
18C ON WIND AND SOUND.
and I think at our next meeting we may enter upon
the subject of optics.
We have now considered the effects produced by
the wide and extended agitation of the air ; but there
is another kind of agitation of which the air is suscep-
tible— a sort of vibratory trembling motion, which,
striking on the drum of the ear, produces sound.
Caroline. Is not sound produced by soHd bodies ?
The voice of animals, the ringing of bells, musical
instruments, are all solid bodies. I know of no sound
"but that of the wind which is produced by the air.
Mrs. B. Sound, I assure you, results from a tre-
mulous motion of the air ; and the sonorous bodies
you enumerate are merely the instruments by which
that peculiar species of motion is communicated to
the air.
Caroline. What! when I ring this little bell, is it
the air that sounds, and not the bell?
Mrs. B. Both the bell and the air are concerned
in the production of sound. But sound, strictly
Speaking, is a perception excited in the mind by the
motion of the air on the nerves of the ear ; the air,
therefore, as well as the sonorous bodies which put
it in motion, is only the cause of sound, the immediate
effect is produced by the sense of hearing ; for, with-
out this sense, there would be no sound.
Emily. I can with difl&culty conceive that. A per-
son born deaf, it is true, has no idea of sound, be-
cause he hears none : yet that does not prevent the
peal existence of sound, as all those who are not deaf
can testify.
Mrs. B. I do not doubt the existence of sound to
all those who possess the sense of hearing ; but it
exists neither in the sonorous body nor in the air, but
in the mind of the person whose ear is struck by the
vibratory motion of the air, produced by a sonorous
body.
To convince you that sound does not exist in sono-
cous bodies, but that air or some other vehicle is ne-
tressary to its production, endeavour to ring the little
ON WIND AUD SOUND. 18^
bell, after I have suspended it under a receiver in the
air-pump, from which I shall exhaust the air
Caroline. This is indeed very strange : though I
agitate it so violently, it does not produce the least
sound.
Mrs. B. By exhausting the receiver, 1 have cut
off the communication between the air and the bell ;
the latter, therefore, cannot impart its motion to the
air.
Caroline. Are you sure that it is not the glass,
which covers the bell, that prevents our hearing it ?
Mrs. B. That you may easily ascertain by letting
the air into the receiver, and then ringing the bell.
Caroline. Very true : I can hear it now almost as
loud as if the glass did not cover it ; and I can no
longer doubt but that air is necessary to the produc-
tion of sound.
Airs. B. Not absolutely necessary, though by far
the most common vehicle of sound. Liquids, as well
as air, are capable of conveying the vibratory motion
of a sonorous body to the organ of hearing ; as sound
can be heard under water. Solid bodies also convey
sound, as I can soon convince you by a very simple
experiment. I shall fasten this string by the middle
round the poker ; now raise the poker from the
ground by the two ends of the string, and hold one to
each of your ears : — I shall now strike the poker with
a ke}^ and you will find that the sound is conve3'ed to
the ear by means of the strings, in a much more per-
fect manner than if it had no other vehicle than the
air.
Caroline. That it is, certainly, for I am almost
stunned by the noise. But what is a sonorous body,
Mrs. B. ? for all bodies are capable of producing
some kind of sound by the motion they communicate
to the air.
Mrs. B. Those bodies are called sonorous, which
produce clear, distinct, regular, and durable sounds,
such as a bell, a drum, musical strings, wind-instru-
ments, &c. They owe this property to their elasti*
188 ©N WIND AND SOUND.
city ; for an elastic body, after having been struck,
not only returns to its former situation, but having
acquired momentum by its velocity, like the pendu-
lum, it springs out on the opposite side. If 1 draw
the string A B, which is made fast at both ends to C,
it will not only return to its original position, but pro-
ceed onwards to D. This is its first vibration, at the
end of which it will retain sufficient velocity to bring
it to E, and back again to F, which constitutes its se-
cond vibration ; the third vibration will carry it only
to G and H, and so on, till the r^istance of the air
destroys its motion.
The vibration of a sonorous body gives a tremu-
lous motion to the air around it, very similar to the
motion communicated to smooth water when a stone
is thrown into it. This first produces a small circu-
lar wave around the spot in which the stone falls j
the wave spreads, and gradually communicates its
motion to the adjacent waters, producing similar
waves to a considerable extent. The same kind of
waves are produced in the air by the motion of a
sonorous body, but with this difference, that as air is
an elastic fluid, the motion does not consist of regu-
larly extending waves, but of vibrations, and are com-
posed of a motion forwards and backwards, similar to
those of the sonorous body. They differ also in the
one taking place in a plane, the other in all direc-
tions. The aerial undulations being spherical.
Emily. But if the air moves backwards as well as
forwards, how can its motion extend so as to convey
sound to a distance ?
Mrs. B. The first sphere of undulations which
are produced immediately around the sonorous body,
by pressing against the contiguous air, condenses it.
The condensed air, though impelled forward by the
pressure, re-acts on the first set of undulations, dri-
ving them back again. The second set of undula-
tions which have been put in motion, in their turn
communicate their motion, and are themselves driven
back by re-action. Thus there is a succession of
v>N WIx\D AND SOUNE». 18&
waves in the air, corresponding with the succession
©f waves in the water.
Caroline. The vibrations of sound must extend
much further than the circular waves in water, since
sound is conveyed to a great distance.
Mrs. B. The air is a fluid so much less dense
than water, that motion is more easily communicated
to it. The report of a cannon produces vibrations
of the air, which extend to several miles around.
Emily. Distant sound takes some time to reach
us, since it is produced at the moment the cannon is
fired ; and we see the light of the flash long before
we hear the report.
Mrs. B. The air is immediately put in motion by
the firing of a cannon ; but it requires time for the
vibrations to extend to any distant spot. The veloci-
ty of sound is computed to be at the rate of 1142
feet in a second.
Caroline. With what astonishing rapidity the vi-
brations must be communicated ! But the velocity of
sound varies, I suppose, with that of the air which
conveys it. If the wind sets towards us from the
cannon, we must hear the report sooner that if it set
the other waj'.
Mrs. B. The direction of the wind makes less difl*er-
ence in the velocity of sound than you would imagine,
if the wind sets from us, it bears most of the aerial
waves away, and renders the sound fainter ; but it is
not very considerably longer in reaching the ear than
if the wind blew towards us. This uniform velocity
of sound enables us to determine the distance of the
object trom which it proceeds ; as that of a vessel at
sea firing a cannon, or that of a thunder cloud. If
we do no not hear the thunder till half a minute after
we see the lightning, we conclude the cloud to be at
the distance of six miles and a half.
Emily. Pray how is the sound of an echo pro-
duced ?
Mrs. B. When the aerial vibrations meet with an
obstacle, having a hard and regular surface, such as a
190 ON WIND AND SOUND.
wall, or rock, they are reflected back to the ear, and
produce the same sound a second time ; but the sound
will then appear to proceed from the object by which
it is reflected. If the vibrations fall perpendicularly
on the obstacle, they are reflected back in the same
line ; if obliquely, the sound returns obliquely in the
opposite direction, the angle of reflection being
equal to the angle of incidence
Caroline. Oh, then, Emily, I now understand why
the echo of my voice behind our house is heard so
much plainer by you than it is by me, when we stand
at the opposite ends of the gravel walk. My voice,
or rather, 1 should say, the vibrations of air it occa-
sions, fall obliquely on the wall of the house, and
are reflected by it to the opposite end of the gravel
walk.
Emily. Very true ; and we have observed, that
when we stand in the middle of the walk, opposite
the house, the echo returns to the person who spoke.
Mrs. B. Speaking-trumpets are constructed on the
principle of the reflection of sound. The voice, instead
ofbeingdiff'usedinthe open air, is confined within the
trumpet ; and the vibrations, which spread and fall
against the sides of the instrument, are reflected ac-
cording to the angle of incidence, and fall into the direc-
tion of the vibrations which proceed straight forwards.
The whole of the vibrations are thus collected into a
focus ; and if the ear be situated in or near thkt spot,
the sound is prodigiously increased. Figure 7. Plate
XIV. will give you a clearer idea of the speaking-
trumpet : the reflected rays are distinguished from
those of incidence, by being dotted ; and they are
brought to a focus at F. The trumpet used by deaf
persons acts on the same principle ; but as the voice
enters the trumpet at the large, instead of the small
end of the instrument, it i? not so much confined, nor
the sound so much increased.
Emily. Are the trumpets used as musical instru-
ments also constructed on this principle ?
Mrs. B. So far as their form tends to increase the
V
ON WIND AND SOUNIK 191
sound, they are ; but, as a musical instrument, the
trumpet becomes itself the sonorous body, which is
made to vibrate by blowing into it, and communicates
its vibrations to the air.
I will attempt to give you, in a few words, some no-
tion of the nature of musical sounds, which, as you
are fond of music, must be interesting to you.
if a sonorous body be struck in such a manner,
that its vibrations are all performed in regular times,
the vibrations of the air will correspond with them ;
and striking in the same regular manner on the drum
of the ear, will produce the same uniform sensation on
the auditory nerve, and excite the same uniform idea
in the mind ; or, in other words, we shall hear one
musical tone.
But if the vibrations of the sonorous body are irre-
gular, there will necessarily follow a confusion of aeri-
al vibrations ; for a second vibration may commence
before the first is finished, to meet it half way on its
return, interrupt it in its course, and produce harsh
jarring sounds, which are called discords.
Emily. But each set of these irregular vibrations,
if repeated at equal intervals, would, 1 suppose, pro-
duce a musical tone ? It is only their irregular suc-
cession which makes them interfere, and occasions
discord.
Mrs B. Certainly. The quicker a sonorous bo-
dy vibrates, the more acute, or sharp, is the sound
produced.
Caroline. But if I strike any one note of the piano-
forte repeatedly, whether quickly or slowly, it al-
ways gives the same tone.
Mrs. B. Because the vibrations of the same
string at the same degree of tension, are always of a
similar duration. The quickness or slowness of the
vibrations relate to the single tones, not to the vari-
ous sounds which they may compose by succeeding
each other. Striking the note in quick succession,
produces a more frequent repetition of the tone, but
does not increase tlie velocity of the vibrations of the
192 ONT WIND AND 30UND.
string. The duration of the vibrations of strings or
chords, depends upon their length, their thickness or
weight, and their degree of tension : thus, you find,
the low bass notes are produced by long, thick, loose
strings ; and the high treble notes by short, small, and
tight strings.
Caroline. Then the different length and size of
the strings of musical instruments, serves to vary the
duration of the vibrations, and consequently, the
acuteness or gravity of the notes ?
Mrs. B. Yes. Among the variety of tones, there
are some which, sounded together, please the ear,
producing what we call harmony, or concord. This
arises from the agreement of the vibrations of the
two sonorous bodies ; so that some of the vibrations
of each strike upon the ear at the same time. Thus, if
the vibrations of two strings are performed in equal
times, the same tone is produced by both, and they
are said to be in unison.
Emily. Now, then, I understand why, when I
tune my harp in unison with the piano-forte, I draw
the strings tighter if it is too low, or loosen them if it
is at too high a pitch ; it is in order to bring them to
vibrate, in equal times, with the strings of the piano-
forte.
J\Jrs. B. But concord, you know, is not confined
to unison ; for two different tones harmonize in a va-
riety of cases. If the vibrations of one string (or
sonorous body whatever) vibrate in double the time
of another, the second vibration of the latter will
strike upon the ear at the same instant as the first vi-
bration of the former ; and this is the concord of an
octave.
If the vibrations of two strings are as two to
three, the second vibration of the first corresponds
with the third vibration of the latter, producing the
harmony called a fifth.
Caroline. So, then, when I strike the key-note
with its fifth, I hear every second vibration of one,
and every third of the other at the same time ?
ON WIND AND SOUN». 10^
Mrs. B. Yes ; and the key-note struck with the
fourth is likewise a concord, hecause the vibrations
are as three to four. The vibrations of a major third
with the key-note, are as four to tive ; and those of
a minor third, as five to six.
There are other tones which, though they cannot
be struck together without producing discord, if
struck successively give us the pleasure which is call-
ed melody. Upon these general principles the sci-
ence of music is founded ; but I am not sufliciently
acquainted with it to enter any further into it.
We shall now, therefore, take leave of the subject
of sound ; and, at our next interview, enter upon
that of optics, in which we shall consider the nature
of vision, light, and colours.
17
CONVERSATION XIV,
ON OPTICS.
Of Luminous, Transparent, and Opaque Bodies. — Of
the Radiation of Light. — Of Shadows. — Of the Re-
flection of Light. — Opaque Bodies seen only by Re-
fleeted Light. — Vision Explained. — Camera ObscU'
ra. — Image of Objects on the Retina.
CAROLINE. I long to begin our lesson to day,
Mrs. B., for 1 expect that it will be very entertaining.
Mrs. B. Optics is certainly one of the most in-
teresting branches of Natural Philosophy, but not one
of the easiest to understand ; I must therefore beg
that you will give me the whole of your attention.
I shall first inquire, whether you comprehend the
meaning of a luminous body, an opaque body, and a
transparent body.
Caroline. A luminous body is one that shines ; an
opaque . . .
Mrs. B. Do not proceed to the second, until we
have agreed upon the definition of the first. All bo-
dies that shine are not luminous ; for a luminous body
is one that shines by its own light, as the sun, the fire,
a candle, &c.
Emily. Polished metal then, when it shines with
so much brilliancy, is not a luminous body ?
Mrs. B. No, for it wouM be dark if it did not re-
ceive light from a luminous body ; it belongs, there-
fore, to the class of opaque or dark bodies, which
Fig. 1.
fzatJ^
^ ^^
ON OPTICS. 195
comprehend all such as are neither luminous nor will
admit the light to pass through them.
Emily. And transparent bodies are those which
admit the light to pass through them ; such as glass
and water ?
Mrs. B» You are right. Transparent or pellucid
bodies are frequently called mediums ; and the rays
of light which pass through them are said to be
transmitted by them.
Light, when emanated from the sun, or any other
luminous body, is projected forwards in straight lines
in every possible direction : so that the luminous
body is not only the general centre from whence all
the rays proceed ; but every point of it may be con-
sidered as a centre which radiates light in every di-
rection. (Fig. 1. Plate XV.)
Emily. But do not the rays which are projected
in different directions, and cross each other, interfere
and impede each other's course ?
Mrs. B. Not at all. The particles of light are so
extremely minute, that they are never known to in-
terfere with each other. A ray of light is a single
line of light projected from a luminous body ; and a
pencil of rays is a collection of rays proceeding from
any one point of a luminous body, as fig. 2.
Caroline. Is light then a substance composed of
particles like other bodies ?
Mrs. B. That is a disputed point upon which I
cannot pretend to decide. In some respects, light is
obedient to the laws which govern bodies ; in others,
it appears to be independent of them ; thus, though
its course is guided by the laws of motion, it does
not seem to be influenced by those of gravity. It
has never been discovered to have weight, though a
variety of interesting experiments have been made
with a view of ascertaining that point ; but we are
so ignorant of the intimate nature of light, that an at-
tempt to investigate it would lead us into a labyrinth
of perplexity, if not of error ; we shall therefore
196 ON OPTICS.
i5onfine our attention to those properties of light
which are well ascertained.
Let us return to the examination of the effects of
the radiation of light from a luminous body. Since
the rays of light are projected in straight lines, when
they meet with an opaque body through which they
are unable to pass, they are stopped short in their
course ; for they cannot move in a curve line round
the body.
Caroline. No, certainly ; for it would require
some other force besides that of projection to pro-
duce motion in a curve line.
Mrs. B. The interruption of the rays of light, by
the opaque body, produces, therefore, darkness on
the opposite side of it ; and if this darkness fall upon
a wall, a sheet of paper, or any object whatever, it
forms a shadow.
Emily. A shadow then, is nothing more than
darkness produced by the intervention of an opaque
body, which prevents the rays of light from reaching
an object behind the opaque body.
Caroline. Why then are shadows of different de-
grees of darkness ; for I should have supposed from
your definition of a shadow, that it would have been
perfectly black ?
Mrs. B. It frequently happens that a shadow is
produced by an opaque body interrupting the course
of the rays from one luminous body, while light
from another reaches the space where the shadow is
formed, in which case the shadow is proportionally
fainter. This happens if the opaque body be lighted
by two candles : if you extinguish one of them, the
shadow will be both deeper and more distinct.
Caroline. But yet it will not be perfectly dark.
Mrs. B. Because it is still slightly illumined by
light reflected from the walls of the room, and other
surrounding objects.
You must observe, also, that when a shadow is
produced by the interruption of rays from a single
ON OPTICS. 197
luminous body, the darkness is proportional to the
intensity of the light.
Emily. I should have supposed the contrary ; for
as the light reflected from surrounding objects on the
shadow, must be in proportion to the intensity of the
light, the stronger tlie light the more the shadow
will be illumined.
Mrs. B. Your remark is perfectly just ; but as
we have no means of estimating the degrees of light
and of darkness but by comparison, the strongest
light will appear to produce the deepest shadow. —
Hence a total eclipse of the sun occasions a more sen-
sible darkness than midnight, as it is immediately
contrasted with the strong light of noonday.
Caroline. The re-appearance of the sun after an
eclipse must, by the same contrast, be remarkably
brilliant.
Mrs. B. Certainly. There are several things to
be observed in regard to the form and extent of sha-
dows. If the luminous body A (fig. 3.) is larger than
the opaque body B, the shadow will gradually di-
minish in size, till it terminate in a point.
Caroline. This is the case with the shadows of
the earth and the moon, as the sun which illumines
them is larger than either of those bodies. And
why is it not the case with the shadows of terrestrial
objects, which are equally illumined by tffe sun ?
but their shadows, far from diminishing, are always
larger than the object, and increase with the dis-
tance from it.
Mrs. B. In estimating the effect of shadows, we
must consider the apparent not the real dimensions
of the luminous body ; and in this point of view, the
sun is a small object compared with the generality of
the terrestrial bodies which it illumines : and when
the luminous body is less than the opaque body, the
shadow will increase with the distance to infinity.
All objects, therefore, which are apparently larger
than the sun, cast a maccnified shadow. This will
17*
198 ON OPTICA.
be best exemplified, by observing the shadow oi au
object lighted by a candle.
Emily. I have often noticed, that the shadow of
my figure against the wall, grows larger as it is more
distant from me, which is owing, no doubt, to the can-
dle that shines on me being much smaller than my-
self?
Mrs. B. Yes. The shadow of a figure A, (fig. 4,)
varies in size, according to the distance of the several
surfaces B C D E, on which it is described.
Caroline. 1 have observed, that two candles pro-
duce two shadows from the same object ; whilst it
would appear, from what you said, that they should
rather produce only half a shadow, that is to say, a
very faint one.
Mrs. B. The number of lights (in different direc-
tions) while it decreases the intensity of the sha-
dow, increases their number, which always corres-
ponds with that of the lights ; for each light makes
the opaque body cast a different shadow, as illustrated
by figure 5. It represents a ball A, lighted by three
candles B, C, D, and you observe the light B pro-
duces the shadow 6, the light C the shadow c, and the
light D the shadow d.
Emily. I think we now understand the nature of
shadows very well ; but pray what becomes of the
rays oi^ light which opaque bodies arrest in their
course, and the interruption of which is the occasion
of shadows ?
Mrs. B. Your question leads to a very important
property of light. Reflection. When rays of light
encounter an opaque body, which they cannot tra-
verse, part of them are absorbed by it, and part are
leflected, and rebound just as an elastic ball which is
struck against a wall.
Emily. And is light in its reflection governed by
the same laws as solid elastic bodies ?
Mrs. B. Exactly. If a ray of light fall perpendi-
eularly on an opaque body, it is reflected back in the
same line, towards the point whence it proceeded.
ON OPTICSi 191*
If it fall obliquely, it is reflected obliquely, but in the
opposite direction ; the angle of incidence being equal
to the angle of reflection. You recollect that law in
mechanics ?
Emily. Oh yes, perfectly,
Mrs. B. If you will shut the shutters, we shall
admit a ray of the sun's light through a very small
aperture, and I can show you how it is reflected, i
now hold this mirror, so that the ray shall fall per-
pendicularly upon it.
Caroline. I see the ray which falls upon the mir-
ror, but not that which is reflected by it.
Mrs. B. Because its reflection is directly retro-
grade. The ray of incidence and that of reflection
both being in ti»e same line, though in opposite direc-
tions, are confounded together.
Emily. The ray then which appears to us single,
is really double, and is composed of the incident ray
proceeding to the mirror, and of the reflected ray re-
turning from the mirror.
Mrs. B. Exactly so. We shall now separate them,
by holding the mirror M, (fig. 6,) in such a manner,
that the incident ray A B shall fall obliquely upon it
— you see the reflected ray B C, is marching off" in
another direction. If we draw a line from the point
of incidence B, perpendicular to the mirror, it will
divide the angle of incidence from the angle of re-
flection, and you will see that they are equal.
Emily. Exactly ; and now that you hold the mir-
ror so, that the ray falls more obliquely on it, it is
also reflected more obliquely, preserving the equality
of the angles of incidence and reflection.
Mrs. B. It is by reflected rays only that we see
opaque objects. Luminous bodies send rays of light
immediately to our eyes, but the rays which they
send to other bodies are invisible to us, and are seen
only when they are reflected or transmitted by those
bodies to our eyes.
Emily. But have we not just seen the ray of light
in its passage from the sua to the mirror^ and its re-
200 ON OPTICS.
flection ? yet in neither case were those rays in a di-
rection to enter our eyes.
Mrs. B. No. What you saw was the light reflect-
ed to your eyes by small particles of dust floating in
the air, and on which the ray shone in its passage to
and from the mirror.
Caroline. Yet I see the sun shining on that house
yonder, as clearly as possible.
Mrs. B. Indeed you cannot sec a single ray which
passes from the sun to the house ; you see no rays
but those whicli enter your eyes ; therefore it is the
rays which are reflected by the house to you, and not
those which proceed from tlie sun to the house, that
are visible to you.
Caroline. Why then does one side of the house
appear to be in sunshine, and the other in the shade ?
for if I cannot see the sun shine upon it, the whole of
the house should appear in the shade.
Mrs. B. That side of the house which the sun
shines upon, reflects more vivid and luminous rays
than the side which is in shadow, for the latter is illu-
mined only by rays reflected upon it by other objects,
these rays are therefore twice reflected before they
reach your sight ; and as light is more or less absorb-
ed by the bodies it strikes upon, every time a ray is
reflected its intensity is diminished.
Caroline. Still I cannot reconcile myself to the
idea, that we do not see the sun's rays shining on ob-
jects, but only those which objects reflect to us.
Mrs. B. I do not, however, despair of convincing
you of it. Look at that large sheet of water, can you
tell me why the sun appears to shine on one part of
it only ?
Caroline. No, indeed ; for the whole of it is equal-
ly exposed to the sun. This partial brilliancy of wa-
ter has often excited my wonder ; but it has struck
me more particularly by moonlight. I have fre-
quently observed a vivid streak of moonshine on the
sea, while the rest of the water remained in deep
obscurity, and yet there was no apparent obstacle to
ON OPTICS. 201
prevent the moon from shining on every part of the
water equally.
Mrs. B. By moonlight the effect is more remark-
able, on account of the deep obscurity of the other
parts of the water ; while by the sun's light the ef-
fect is too strong for the eye to be able to contem*-
plate it.
Caroline, But if the sun really shines on every
part of that sheet of water, why does not every
part of it reflect rays to my eyes ?
Mrs. B. The reflected rays are not attracted out
of their natural course by your eyes. The direction
of a reflected ray, you know, depends on that of the
incident ray ; the sun's rays, therefore, which fall
with various degrees of obliquity upon the water, are
reflected in directions equally various ; some of these
will meet your eyes, and you will see them, but those
which fall elsewhere are invisible to you.
Caroline. The streak of sunshine, then, which
we now see upon the water, is composed of those
rays which by their reflection happen to fall upon my
eyes ?
Mrs. B. Precisely.
Emily. But is that side of the house yonder, which
appears to be in shadow, really illumined by the sun,
and its rays reflected another way ?
Mrs. B. No ; that is a diff'erent case from the
sheet of water. That side of the house is really in
shadow ; it is the west side, which the sun cannot
shine upon till the afternoon.
Emily. Those objects, then, which are illumined
by reflected rays, and those which receive direct rays
from the sun, but which do not reflect those rays to-
wards us, appear equally in shadow ?
Mrs. B. Certainly ; for we see them both illu-
mined by reflected rays. That part of the sheet of
water, over which the trees cast a shadow, by what
light do you see it ?
Emily. Since it is not by the sun's direct rays, it
202 ON OPTICS.
must be by those reflected on it from other objects,
and which it again reflects to us.
Caroline. But if we see all terrestrial objects by
reflected light, (as we do the moon,) why do they ap-
pear so bright and luminous ? 1 should have suppos-
ed that reflected rays would have been dull and faint,
like those of the moon.
Mrs. B. The moon reflects the sun's light with as
much vividness as any terrestrial object. If you
look at it on a clear night, it will appear as bright as
a sheet of water, the walls of a house, or any object
seen by daylight, and on which the sun shines. The
rays of the moon are doubtless feeble, when compar-
ed with those of the sun ; but that would not be a
fair comparison, for the former are incident, the lat-
ter reflected rays.
Caroline. True ; and when we see terrestrial ob-
jects by moonlight, the light has been twice reflected,
and is consequently proportionally fainter.
Mrs. B. In traversing the atmosphere, the rays,
both of the sun and moon, lose some of their light. ^
For though the pure air is a transparent medium,
which transmits the rays of light freely, we have ob-
served, that near the surface of the earth it is loaded
with vapours and exhalations, by which some portion
of them are absorbed.
Caroline. I have often noticed, that an object oq
the summit of a hill appears more distinct than one
at an equal distance in a valley, or on a plain ; which is
owing, I suppose, to the air being more free from va-
pours in an elevated situation, and the reflected rays
being consequently brighter.
Mrs. B. That may have some sensible effect ; but
when an object on the summit of a hill has a back
ground of light sky, the contrast with the object
makes its outline more distinct.
Caroline. I now feel well satisfied, that we see
opaque objects only by reflected rays ; but I do not
understand how these rays show us the objects from
which they proceed ?
ON OPTICS. 203
Mrs, B. The rays of li^ht enter at the pupil of
the eye, and proceed to the retina, or optic nerve,
which is situated at the back part of the eye-ball ;
and there they describe the (isjure, colour, and (ex-
cepting size) form a perfect representation of the ob-
ject from which they proceed. We shall again dose
the shutters, and admit the light through the small
aperture, and yo ; will see a picture on the wall, op-
posite the ap«*rture, similar to that which is delinea-
ted on the retina of the eye.
Caroline. Oh, how wonderful! There is an exact
picture in miniature of the garden, the gardener at
work, the trees blown about by the wind. The
landscape would be perfect, if it were not reversed ;
the ground being ab )ve. and the sky beneath.
Mrs. B. Is it not enough to admire, you must un-
derstand this phenomenon, which is called a camera
obscura, from the necessity of darkening the room, in
order to exhibit it.
This picture is produced by the rays of light re-
flected from the various objects in the garden, and
which are admitted through the hole in the window-
shutter.
The rays from the glittering weathercock at the
top of the alcove A, (Plate XVI. fig. 1.) represent it in
this spot a; for the weathercock being much higher
than the aperture in the shutter, only a few of the
rays, which are reflected by it in an obliquely de-
scending direction, can find entrance there. The
rays of light, you know, always move in straight
lines ; those, therefore, which enter the room in a
descending direction, will continue their course in
the same direction, and will, consequently, fall upon
the lower part of the wall opposite the aperture, and
represent the weathercock reversed in that spot, in-
stead of erect in the uppermost part of the landscape.
Emily. And the rays of light from the steps (B)
of the alcove, in entering the aperture, ascend, and
will describe those steps in the highest instead of the
lowest part of the landscape.
204 ©N OPTICS.
Mrs. B. Observe, too, that the rays coming from
the alcove, which is to our left, describe it on the
wall to the right ; while those which are reflected by
the walnut-tree C D, to our right, delineate its figure
in the picture to the left, c d. Thus the rays, cona-
ing in different directions, and proceeding always in
right lines, cross each other at their entrance through
the aperture: those which come above proceed be-
low, those from the right go to the left, those from
the left towards the right ; thus every object is re-
presented in tlie picture, as occupying a situation the
very reverse of that which it does m nature.
Caroline. Excepting the flower-pot E F, which,
though its position is reversed, has not changed its
situation in the landscape.
Mrs. B. The flower-pot is directly in front of the
aperture ; so that its rays fall perpendicularly upon
it, and, consequently, proceed perpendicularly to the
wall, where they delineate the object directly behind
the aperture.
Emily. And is it thus that the picture of objects is
painted on the retina of the eye ?
Mrs. B. Precisely. The pupil of the eye,
through wliich the rays of light enter, represents the
aperture in the window-shutter ; and the image deli-r
neated on the retina, is exactly similar to the picture
on the wall.
Caroline. You do not mean to say, that we see only
the representation of the object which is painted oq
the retina, and not the object itself?
Mrs. B. If, by sight, you understand that sense
by which the presence of objects is perceived by the
mind, through the means of the eyes, we certainly
see only the image of those objects painted on the
retina.
Caroline. This appears to me quite incredible.
Mrs. B. The nerves are the only part of our
frame capable of sensation : they appear, therefore^
to be the instruments which the mind employs in its
perceptions : for a sensation always conveys an idea
J'LATE. JCVI.
/h
A
/ ^ H \
\
ON OPTICS. 205
to the mind. Now it is known, that our nerves can
be affected only by contact ; and for this reason the
organs of sense cannot act at a distance : for instance,
we are capable of smelling only particles which are
actually in contact with the nerves of the nose. We
have already observed, that the odour of a flower
consists in etfluvia, composed of very minute particles,
which penetrate the nostrils, and strike upon the ol-
factory nerves, which instantly convey the idea of
smell to the mind.
Emily. And sound, though it is said to be heard at
a distance, is, in fact, heard only when the vibrations
of the air, which convey it to our ears, strike upon
the auditory nerve.
Caroline. There is no explanation required, to
prove that the senses of feeling and of tasting are ex-
cited only by contact.
Mrs. B. And I hope to convince you, that the
sense of sight is so likewise. The nerves, which
constitute the sense of sight, are not different in their
nature from those of the other organs ; they are
merely instruments which convey ideas to the mind,
and can be affected only on contact. Now, since real
objects cannot be brought to touch the optic nerve,
the image of them is conveyed thither by the rays of
light proceeding from real objects, which actually
strike upon the optic nerve, and form that image which
the mind perceives.
Caroline. While I listen to your reasoning, I feel
convinced ; but when I look upon the objects around,
and think that I do not see them, but merely their
image painted in my eyes, my belief is again stagger-
ed. I cannot reconcile myself to the idea, that 1 do
not really see this book which I hold in my hand, nor
the words which I read in it.
Mrs. B. Did it ever occur to you as extraordina-
ry, that you never beheld your own face ?
Caroline. No ; because I so frequently see an ex-
act representation of it in the looking-glass.
v¥r<?. B. You see a far more exact representation
18
206 ox OPTICS.
©f objects on the retina of your eye : it is a much
more perfect mirror than any made by art.
Emily. But is it possible, that the extensive land-
scape, which I now behold from the window, should
be represented on so small a space as the retina of
the eye ?
Mrs. B. It would be impossible for art to paint so
small and distinct a miniature ; but nature works with
a surer hand, and a more delicate pencil. That pow-
er, which forms the feathers of the butterfly, and the
flowerets of the daisy, can alone portray so admira-
ble and perfect a miniature as that which is represent-
ed on the retina of the eye.
Caroline, But, Mrs. B., if we see only the image
of objects, why do we not see them reversed, as you
showed us they were in the camera obscura ? Is not
that a strong argument against your theory ?
Mrs, B. Not an unanswerable one, I hope. The im-
age on the retina, it is true, is reversed, like that in the
camera obscura ; as the rays, unless from a very small
object, intersect each other on entering the pupil in
the same manner as they do on entering the camera
obscura. The scene, however, does not excite the
idea of being inverted, because we always see an ob-
ject in the direction of the rays which it sends to us.
Emily. I confess I do not understand that.
Mrs. B. It is, r think, a diflicult point to explain
clearly. A ray which comes from the upper part of
an object, describes the image on the lower part of
the retina ; but experience having taught us, that the
direction of that ray is from above, we consider that
part of the object it represents as uppermost. The
rays proceeding from the lower part of an object fall
upon the upper part of the retina; but as we know their
direction to be from below, we see that part of the ob-
ject they describe as the lowest.
Caroline. When 1 want to see an object above me,
I look up ; when an object below me, I look down.
Does not this prove that I see the objects themselves?
for if I beheld only the image, there would be no
osr OPTICS'. 207
necessity for looking up or down, according as the
©bject was higher or lower than myself.
Mrs. B. I beg your pardon. When you look up to
an elevated object, it is in order that the rays reflect-
ed froKi it should fall upon the retina of your eyes ;
but the very circumstance of directing you eyes up-
wards convinces you that the object is elevated, and
teaches you to consider as uppermost the image it
forms on the retina, though it is, in fact, represented
in the lowest part of it. When you look down up-
on an object, you draw 3'^our conclusion from a simi-
lar reasoning ; it is thus that we see all objects in the
direction of the rays which reach our eyes.
But I have a further proof in favour of what I
have advanced, which, I hope, will remove your re-
maining doubts ; I shall, hovvever, defer it till our
next meeting, as the lesson has been sulBciently long'.
to-day.
CONVERSATION XV.
OTTlCS^continued.
ON THE ANGLE OF VISION, AND THE
REFLECTION OF MIRRORS.
Angle of Vision. — Reflection of Plain Mirrors. •-' Re-
flection of Convex Mirrors. — Reflection of Concave
Mirrors.
CAROLINE. Well, Mrs. B., I am very impatient
to hear what further proofs you have to offer in sup-
port of your theory. You must allow that it was
rather provoking to dismiss us as you did at our last
meeting.
Mrs. B. You press so hard upon me with your
objections, that you must give me time to recruit my
forces.
Can you tell me, Caroline, why objects at a dis-
tance appear smaller than they really are ?
Caroline. I know no other reason than their dis-
tance.
Mrs. B. I do not think I have more cause to be
satisfied with your reasons than you appear to be
with mine. We must refer again to the camera ob-
scura to account for this circumstance ; and 3'ou will
iind, that the different apparent dimensions of objects
at different distances, proceed from our seeing, not
the objects themselves, but merely their image on
the retina. Fig. 1. Plate XVII. represents a row of
PLATE. XV,
ON THE ANGLE OF VISION. 209
trees, as viewed in the camera obscura. I have ex-
pressed the direction of the rays, from the objects to
the image, by lines. Now, observe, the ray which
comes from the top of the nearest tree, and that
which comes from the foot of the same tree, meet at
the aperture, forming an angle of about twenty-five
degrees ; this is called the angle of vision, under
which we see the tree. These rays cross each
other at the aperture, forming equal angles on each
side'of it, and represent the tree inverted in the ca-
mera obscura. The degrees of the image are consi-
derably smaller than those of the object, but the pro-
portions are perfectly preserved.
Now let us notice the upper and lower ray, from
the most distant tree ; they form an angle of not more
than twelve or fifteen degrees, and an image of pro-
portional dimensions. Thus, two objects of the same
size, as the two trees of the avenue, form figures of
different sizes in the camera obscura, according to
their distance ; or, in other words, according to the
angle of vision under which they are seen. Do yoa
understand this ?
Caroline. Perfectly.
Mrs. B. Then you have only to sappose that the
representation in the camera obscura is similar to that
on the retina.
Now since objects of the same magnitudes appear
to be of different dimensions, when at different distan-
ces from us, let me ask you, which it is that we see j
the real objects, which we know do not vary in size,
or the images, which we know do vary according to
the angle of vision under which we see them ?
Caroline. I must confess, that reason is in favour
of the latter. But does that chair at the further end
of the room form an image on my retina much smaller
than this which is close to me ? they appear exactly
of the same size.
Mrs. B. 1 assure you they do not. The expe-
rience we acquire by the sense of touch corrects the
errors of our sight with regard to objects withiu our
18*
210 ON THE ANGLE OF VISIOTC.
reacli. You are so perfectl}? convinced of the real
size of objects which }'ou can handle, that 3'ou do not
attend to their apparent difference.
Does that house appear to you much smaller than
when you are close to it ^
Caroline, No, because it is very near us.
Mrs. B. And yet you can see the whole of it
through one of the windows of this room. The
image of the house on your retina must, therefore,
be smaller than that of the window through which
you see it. It is your knowledge of the real size of
the house which prevents your attending to its appa-
rent magnitude. If you were accustomed to draw
from nature, you would be fully aware of this differ-
ence. ^
Emily. And pray, what is the reason that, when
we look up an avenue, the trees not only appear
smaller as they are more distant, but seem gradually
to approach each other till they meet in a point?
Mrs. B. Not only the trees, but the roiid which
separates the two rows, forms a smaller visual angle,
in proportion as it is more distant from us ; there-
fore the width of the road gradually diminishes as
well as the size of the trees, till at length the road
apparently terminates in a point, at which the trees
seem to meet.
But this effect of the angle of vision will be more
fully illustrated by a little model of an avenue, which
I have made for that purpose. It consists of six
trees, leading to a hexagonal temple, and viewed by
an eye, on the retina of which the picture of the
objects is delineated.
I beg that you will not criticise the proportions ;
for though the eye is represented the size of life,
while the trees are not more than three inches high,
the disproportion does not affect the principle which
the model is intended to elucidate.
Emily. The threads which pass from the objects
through the pupil of the eye to the retina, are, I sup-
ON TH£ ANGLE OF VISI©.\. 211
pese, to represent the rays of light which convey the
image of the objects to the retina ?
Mrs. B. Yes. i have been obhged to limit the
rays to a very small number, in order to avoid confu-
sion ; there are, you see, only two from each tree.
Caroline. But as one is from the summit, and the
other from the foot of the tree, they exemplify the
different angles under which we see objects at differ-
ent distances, better than if there were more.
Airs. B. There are seven rays proceeding from
the temple, one from the summit, and two from each
of the angles that are visible to the eye, as it is situ-
ated ; from these you may form a just idea of the
difference of the angle of vision of objects viewed
obliquely, or in front ; for though the six sides of the
temple are of equal dimensions, that which is oppo-
eite to the eye is seen under a much larger angle
than those which are viewed obliquely. It is on this
principle that the laws of perspective are founded.
Emily. I am very glad to know that, for I have
lately begun to learn perspective, which appeared to
me a very dry study ; but now that 1 am acquainted
with the principles on which it is founded, I shall
find it much more interesting.
Caroline. In drawing a view from nature, then,
we do not copy the real objects, but the image they
form on the retina of our eyes ?
Mrs. B. Certainly. In sculpture, we copy nature
as she really exists ; in painting, we represent her as
she appears to us. It was on this account that 1 found
it difficult to explain, by a drawing, the effects of the
angle of vision, and was under the necessity of con-
structing a model for that purpose.
Emily. 1 hope you will allow us to keep this mo-
del some time, in order to study it more completely,
for a great deal may be learned from it; it illustrates
the nature of the angle of vision, the apparent dimi-
nution of distant objects, and the inversion of the
image on the retina. But pray, why are the threads.
212 ON THE ANGLE OF VISION.
that represent the rays of light coloured, the same as
the objects from which they proceed ?
Mrs. B. That is a question which you must excuse
my answering at present, but I promise to explain it
to you in due time.
I consent very willingly to your keeping the model,
on condition that you will make an imitation of it, on
the same principle, but representing different objects.
We must now conclude the observations that re-
main to be made on the angle of vision.
If an object, with an ordinary degree of illumina-
tion, does not subtend an angle of more than two se-
conds of a degree, it is invisible. There are conse-
quently two cases in which objects may be invisible,
either if they are too small, or so distant as to form
an angle less than two seconds of a degree.
In like manner, if the velocity of a body does not
exceed 20 degrees in an hour, its motion is impercep-
tible.
Caroline. A very rapid motion may then be im-
perceptible, provided the distance of the moving body
is sufficiently great.
Mrs. B. Undoubtedly ; for the greater its distance,
the smaller will be the angle under which its motion
will appear to the eye. It is for this reason that the
motion of the celestial bodies is invisible, notwith-
standing their immense velocity. -*
Emily. I am surprised that so great a velocity as
20 degrees an hour should be invisible.
Mrs. B. The real velocity depends altogether on
the space comprehended in each degree ; and this
space depends on the distance of the object, and the
obliquity of its path. Observe, likewise, that we
cannot judge of the velocity of a body in motion un-
less we know its distance ; for supposing two men to
set off at the same moment from A and B, (tig. 2.) to
walk each to the end of their respective lines C and
D; if they perform their walk in the same space of
time, they must have proceeded at a very different
rate, aad yet to an eye situated at £, they will ap>
ON THE ANGLE OF VISION. "213
pear to have moved with equal velocity : because
they will both have gone through an equal number
of degrees, though over a very unequal length of
ground. Sight is an cxtremel}^ useful sense no doubt,
but it cannot always be relied on, it deceives us both
in regard to the size and the distance of objects ; in-
deed our senses would be very liable to lead us into
error, if experience did not set us right.
Emily. Between the two, I think that we contrive
to acquire a tolerably accurate idea of objects.
Mrs. B. At least sufliciently so for the general
purposes of life. To convince you how requisite
experience is to correct the errors of sight, 1 shall
relate to you the case of a young man who was blind
from his infancy, and who recovered his sight at the
age of fourteen, by the operation of couching. At
first, he had no idea either of the size or distance of
objects, but imagined that every thing he saw tough-
ed his eyes ; and it was not till after having repeated-
ly felt them, and walked from one object to another»
that he acquired an idea of their respective dimen-
sions, their relative situations, and their distances.
Carolina/, The idea that objects touched his eyeS
is, however, not so absurd as it at first appears ; for
if we consider that we see only the image of objects,
this image actually touches our eyes.
Mrs. B. That is doubtless the reason of the opi-
nion he formed, before the sense of touch had cor-
rected his judgment.
Caroline. But since an image must be formed on
the retina of each of our eyes, why do we not see
objects double ?
Mrs. B. The action of the rays on the optic
nerve of each eye is so perfectly similar, that they
produce but a single sensation, the mind therefore
receives the same idea, from the retina of both eyes,
and conceives the object to be single.
Caroline. This is difficult to comprehend, and, I
should think, can be but conjectural.
Mrs. B. I can easily convince you, that you have
214 ON THE ANGLE er VISION.
a distinct image of an object formed on the retina of
each eye. Look at the bell-rope, and tell me, do you
see it to the right or the left of the pole of the fire-
skreen ?
Caroline. A little to the right of it.
Mrs. B. Then shut your right eye, and you will
see it to the left of the pole.
Caroline. That is true indeed !
Mrs. B. There are evidently two representations
of the bell-rope in different situations, which must be
owing to an image of it being formed on both eyes ; if
the action of the rays therefore on each retina were
not so perfectly similar as to produce but one sensa-
tion, we should see double, and we tind that to be the
case with many persons who are afflicted with a dis-
ease in one eye, which prevents the rays of light
from affecting it in the same manner as the other.
Emily' Pray, JMrs. B., when we see the image of
an object in a looking-glass, why is it not inverted as
in the camera obscura, and on the retina of the eye ?
Mrs. B. Because the rays do not enter the mirror
by a small aperture, and cross each other, as they do
at the orifice of a camera obscura, or the pupil of the
eye.
When you view yourself in a mirror, the rayS
from your eyes fall perpendicularly upon it, and are
reflected in the same line ; the image is therefore
described behind the glass, and is situated in the
same manner as the object before it.
Emily. Yes, I see tiiat it is ; but the looking-glass
is not nearly so tall as I am, how is it therefore that
I can see the whole of my figure in it ?
Mrs. B. It is not necessary that the mirror should
be more than half your height, in order that you may
8ee the whole of your person in it, (fig. 3.) The
ray of light C D from your eye, which falls perpen-
dicularly on the mirror B D, will be reflected back
in the same line ; but the ray from your feet will
fall obliquely on the mirror, for it must ascend in or-
der to reach it j it will therefore be reflected in the
ON THE ANGLE GF VISION. . 21i5
line D A : and since we view objects in the direc-
tion of the reflected rays, which reach the eye, and
that the image appears at the same distance behind
the mirror that the object is before it, we must con-
tinue the line A D to E, and the line C D to F, at the
termination of which the image will be represented.
Emily. Then I do not understand why I should
not see the whole of my person in a much smaller
mirror, for a ray of light from my feet would always
reach it, though more obliquely.
Mrs, B. True ; but the more obliquely the ray
falls on the mirror, the more obliquely it will be re-
flected ; the ray would therefore be reflected above
your head, and yon could not see it. This is shown
by the dotted line (fig. 3.)
Now stand a little to the right of the mirror, so
that the rays of light from your figure may fall ob-
liquely on it
Emily. There is no image formed of me in the
glass now.
Mrs. B. I beg your pardon, there is ; but you
cannot see it, because the incident rays falling ob-
liquely on the mirror will be reflected obliquely in
the opposite direction, the angles of incidence and of
reflection being equal. Caroline, place yourself in
the direction of the reflected rays, and tell me whe-
ther you do not see Emily's image in the glass ?
Caroline. Let me consider. — In order to look v».
the direction of the reflected rays, I must place n^^ '
self as much to the left of the glass as Emily stanusto
the right of it. — Now 1 see her image, but it is not
straight before me, but before her ; and appears at
the same distance behind the glass, as she is in front
of it.
Mrs. B. You must recollect, that we always see
objects in the direction of the last rays which reach
our eyes. Figure 4. represents an eye looking at the
image of a vase, reflected by a mirror ; it must see it
in the direction of the ray A B, as that is the raj"
216 ON THE ANGLE OF VISION.
which brings the image to the eye ; prolong the ray
to C, and in that spot will the image appear.
Caroline, I do not understand why a looking-glass
reflects the rays of light ; for glass is a transparent
body, which should transmit them ?
J\irs. B. It is not the glass that reflects the rays
which form the image you behold, but the mercury
behind it. The glass acts chiefly as a transparent
case, through which the rays find an easy passage.
Caroline, Why then should not mirrors be made
simply of mercury ?
Mrs. B, Because mercury is a fluid. By amal-
gamating it with tin-foil, it becomes of the consistence
of paste, attaches itself to the glass, and forms in fact a
mercurial mirror, which would be much more perfect
without its glass cover, for the purest glass is never
perfectly transparent : some of the rays therefore are
lost during their passage through it, by being either
absorbed, or irregularly reflected.
This imperfection of glass mirrors has introduced
the use of metallic mirrors, for optical purposes.
Emily. But since all opaque bodies reflect the
rays of light, I do not understand why they are not
all mirrors ?
Caroline. A curious idea indeed, sister ; it would
be very gratifying.to see one's self in every object at
which one looked.
Mrs. B, It is very true that all opaque objects re-
S*\^t light ; but the surface of bodies in general is so
rough and uneven, that their reflection is extremely
irregular, which prevents the rays from forming an
image on the retina. This you will be able to under-
"stand better, when I shall explain to you the nature
of vision, and the structure of the eye.
You may easily conceive the variety of directions
in which rays would be reflected by a nutmeg-grater,
on account of the inequality of its surface, and the
number of holes with which it is pierced. All solid
bodies resemble the nutmeg-grater in these respects,
more or less ; and it is only those which are suscep-
PLATE, xvnr.
ON THE ANGLE OF VISION. S"! 7
tible of receiving a polish, that can be made to reflect
the rays with regularity. As hard bodies are of the
closest texture, the least porous, and capable of taking
the highest polish, they make the best mirrors ;
none, therefore, are so well calculated for this pur-
pose as metals.
Caroline. But the property of regular reflection
is not confined to this class of bodies ; for 1 have of-
ten seen myself in a highly polished mahogany table.
Mrs. B. Certainly ; but as that substance is less
durable, and its reflection less perfect, than that of
metals, 1 believe it would seldom be chosen for the
purpose of a mirror.
There are three kinds of mirrors used in optics ;
the plain or flat, which are the common mirrors we
have just mentioned ; convex mirrors ; and concave
mirrors. The reflection of the two latter is very dif-
ferent from that of the former. The plain mirror,
we have seen, does not alter the direction of the re-
flected rays, and forms an image behind the glass
exactly similar to the object before it. A convex
mirror has the peculiar property of making the re-
flected rays diverge, by which means it diminishes
the image ; and a concave mirror makes the rays con-
verge, and, under certain circumstances, magnifies the
image.
Eiriily. We have a convex mirror in the drawing
room which forms a beautiful miniature picture of
the objects in the room ; and I have often amused
myself with looking at my magnified face in a concave
mirror. But 1 hope you will explain to us why the
one enlarges, while the other diminishes the objects
it reflects.
Airs. B. Let us begin by examining the reflection
of a convex mirror. This is formed of a portion of
the exterior surface of a sphere. When several pa-
rallel rays fall upon it, that ray only which, if pro-
longed, would pass through the centre or axis of the
mirror, is perpendicular to it. In order to avoid con-
fusion, 1 have, in fig. 1. Plat6 XVUl., drawn only
19
218 ON THE ANGLE OF VISION.
three parallel lines, A B, C D, E F, to represent
rays falling on the convex mirror M N ; the middle
ray, you will observe, is perpendicular to the mirror,
the others fall on it obliquely.
Caroline. As the three rays are parallel, why are
they not all perpendicular to the mirror ?
Mrs. B. They would be so to a flat mirror ; but
as this is spherical, no ray can fall perpendicularly
upon it which is not directed towards the centre of
the sphere.
Emily. Just as a weight falls perpendicularly to
the earth when gravity attracts it towards the centre.
Mrs. B. In order, therefore, that rays may fldl
perpendicularly to the mirror at B and F, the rays
must be in the direction of the dotted lines, which,
you may observe, meet at the centre O of the
sphere, of which the mirror forms a portion.
Now can you tell me in what direction the three
rays, A B, C D, E F, will be reflected ?
Emily. Yes, I think so; the middle ray falling
perpendicularly on the mirror, will be reflected in
the same line: the two others falling obliquely, will
be reflected obliquely to G H ; for the dotted lines
you have drawn are perpendiculars, which divide
their angles of incidence and reflection.
Mrs. B. Extremely well, Emily : and since we
see objects in the direction of the reflected ray, we
shall see the image at L, which is the point at which
the reflected rays, if continued through the mirror,
would unite and form an image. The point is equally
distant from the surface and centre of the sphere, and
is called the imaginary focus of the mirror.
Caroline. Pray, what is the meaning of focus ?
Mrs. B. A point at which converging rays unite.
And it is in this case called an imaginary focus ; be-
cause the rays do not really unite at that point, but
only appear to do so : for the rays do not pass through
the mirror, since they are reflected by it.
Emily. I do not yet understand why an object ap-
pears smaller when viewed in a convex mirror.
O-V THE ANGLE OF TISION. 219
J\Irs. B. It is owing to the divergence of the re-
flected rays. You Avdve seen that a convex mirror
converts, by reflection, parallel rays into divergent
rays ; rays that fall upon the mirror divergent, are
rendered still more so by reflection, and convergent
rays are reflected either parallel, or less convergent.
If then an object be placed before any part of a con-
vex mirror, as the vase A B, fig. 2. for instance, the
two rays from its extremities, falling convergent on
the mirror, will be reflected less convergent, and will
not come to a locus till they arrive at C ; then an eye
placed in the direction of the reflected rays will see
the image formed in (or rather behind) the mirror at
a b.
Caroline. But the reflected rays do not appear to
me to converge less than the incident rays. I should
have supposed that, on the contrary, they converged
more, since they meet in a point ?
Mrs. B. They would unite sooner than they actu-
ally do, if they were not less convergent than the in-
cident rays : for observe, that if the incident rays, ia-
Etead of being reflected by the mirror, continued their
course in their original direction, they would come
to a focus at D, which is considerably nearer to the
mirror than at C ; the image is therefore seen under
a smaller angle than the object ; and the more dis-
tant the latter is from the mirror, the less is the
image reflected by it.
You wiH now easily understand the nature of the
reflection of concave mirrors. These are formed of
a portion of the internal surface of a hollow sphere,
and their peculiar property is to converge the rays
©flight.
Can you discover, Caroline, in what direction the
three parallel rays, A B, C D, EF, which fall on the
concave mirror M N, (fig. 3.) are reflected ?
Caroline. I believe I can. The middle ray is
sent back in the same line, as it is in the direction of
the axis of the mirror ; and the two others will be
reflected obliquely, as they fall obhquely on the mir-
^20 ON THE ANGLE OF VISION.
ror. I must now draw two dotted lines perpendicu-
lar to their points of incidence, which will divide
their angles of incidence and reflection ; and in order
that those angles may be equal, the two oblique rays
must be reflected to L, where they will unite with the
middle ray.
Mrs, B. Very well explained. Thus you see,
that when any number of parallel rays fall on a con-
cave mirror, they are all reflected to a focus : for, in
proportion as the rays are more distant from the axis
af the mirror, they fall more obliquely upon it, and
are more obliquely reflected ; in consequence of
which they come to a focus in the direction of the
axis of the mirror, at a point equally distant from the
centre and the surface of the sphere, and this point is
not an imaginary focus, as happens with the convex
mirror, but is the true focus at which the rays unite.
Emily. Can a mirror form more than one focus by
reflecting rays ?
Mrs. B. Yes. If rays fall convergent on a con-
cave mirror, (fig. 4.) they are sooner brought to a
focus, L, than parallel rays ; their focus is therefore
nearer to the mirror M N. Divergent rays are
brought to a more distant focus than parallel rays, as
in figure 5, where the focus is at L ; but the true fo-
cus of mirrors, either convex or concave, is that of
parallel rays, which is equally distant from the cen-
tre, and the surface of the sphere.
I shall now show you the reflection of real rays of
light, by a metallic concave mirror. This is one
made of polished tin, which I expose to the sun, and
fts it shines bright, we shall be able to collect the rays
into a very brilliant focus. I hold a piece of paper
where 1 imagine the focus to be situated ; you may
see by the vivid spot of light on the paper, how much
the rays converge : but it is not yet exactly in the
focus ; as 1 approach the paper to that point, observe
how the brightness of the spot of light increases,
while its size diminishes.
Caroline. That must be occasioned by the rays
ON THE ANGLE OF VISION. 221
becoming closer together. I think ^-ou hold the pa-
per just in the focus now, the light is so small and
dazzling — Oh, Mrs. B., the paper has taken fire!
Airs. B. The rays of light cannot be concentra-
ted, without, at the same time, accumulating a propor-
tional quantity of heat: hence concave mirrors have
obtained the name of burning-mirrors.
Emily. I have often heard of the surprising etfects
of burning-mirrors, and I am quite dehghted to
understand their nature.
Caroline. It cannot be the true focus of the mir-
ror at which the rays of the sun unite, for as they
proceed from a point, they must fall divergent upon
the mirror.
Mrs. B. Strictly speaking, they certainly do. But
when rays come from such an immense distance as
the sun, their divergence is so trifling, as to be im-
perceptible ; and they may be considered as parallel :
their point of union is, therefore, the true focus of
the mirror, and there the image of the object is re-
presented.
Now that I have removed the mirror out of the in-
fluence of the sun's rays, if I place a burning taper in.
the focus, how will its light be reflected ? (Fig. 6.)
Caroline. That, I confess, I cannot say.
Mrs. B. The ray which falls in the direction of
the axis of the mirror, is reflected back in the same
line ; but let us draw two other rays from the focus,
falling on the mirror at B and F ; the dotted lines are
perpendicular to those points, and the two rays will
therefore be reflected to A and E.
Caroline. Oh, now I understand it clearly. The
rays which proceed from a light placed in the focus
of a concave mirror fall div^ergent upon it, and are
reflected parallel. It is exactly the reverse of the
former experiment, in which the sun's rays fell pa-
rallel on the mirror, and were reflected^ to a focus.
Mrs. B. Yes : when the incident rays are paral-
lel, the reflected rays converge to a focus ; when, odl
the contrary, the incident rays proceed from the fo«
19*
222 ON THE ANGLE OF VISION*
cus, they are reflected parallel. This is an impor-
tant law of optics, and since you are now acquainted
with the principles on which it is founded, I hope that
you will not forget it.
Caroline. I am sure that we shall not. But, Mrs.
B., you said that the image was formed in the focus
of a concave mirror ; yet I have frequently seen glass
concave mirrors, where the object has been repre-
sented within the mirror, in the same manner as in a
convex mirror.
Mrs. B. That is the case only when the object is
placed between the mirror and its focus ; the image
then appears magnified behind, or, as you call it,
nvithin the mirror.
Caroline. I do not understand why the image
should be larger than the object.
Mrs. B. It proceeds from the convergent properr
ty of the concave mirror. If an object, A B, (fig. 7.)
be placed between the mirror and its focus, the rays
from its extremities fall divergent on the mirror, and
on being reflected, become less divergent, as if they
proceeded from C : to an eye placed in that situation
the image will appear magnified behind the mirror
^t a b, since it is seen under a larger angle than the
object. .
You now, I hope, understand the reflection of light
by opaque bodies. At our next meeting we shall
enter upon another property of light, no less interest*
ing, which is called refraction.
CONVERSATION XVl:
ON REFRACTION AND COLOURS.
Transmission of Light by Transparent Bodies. — Re-
fraction. — Refraction of the Atmosphere. — Refrac-
tion of a Lens. — Refraction of the Prism. — Of the
Colours of Rays of Light. — Of the Colours of Bodies.
MRS. B. The refraction of light will furnish the
•subject of to-day's lesson.
Caroline. That is a property of which I have not
the faintest idea.
Mrs. B. It is the effect which transparent me-
diums produce on light in its passage through them.
Opaque bodies, you know, reflect the rays, and trans-
parent bodies transmit them; but it is found, that if a
ray, in passing from one medium into another of dif-
ferent density, fall obliquely, it is turned out of its
course.
Caroline. It must then be acted on by some new-
power, otherwise it would not deviate from its first
direction.
Mrs. B. The power which causes the deviation
of the ray appears to be the attraction of the denser
medium. Let us suppose the two mediums to be air
and water ; if a ray of light passes from air into wa-
ter, it is more strongly attracted by the latter on ac-
count of its superior density.
Emily, in what direction does the water attract-
the ray ?
Mrs. B. It must attract it perpendicularly towards
it, Id the same manner as gravity acts on bodies.
224 THE REFRACTION OF LIGHT.
If then a ray A B, (fig. 1. Plate XIX.) fall perpen-
dicularly on water, the attraction of the water acts in
the same direction as the course of the ray ; it will
not therefore cause a deviation, and the ray will pro-
ceed straight on to E. But if it fall obliquely, as the
ray C B, the water will attract it out of its course.
Let us suppose the ray to have approached the surface
of a denser medium, and that it there begins to be af-
fected by its attraction ; this attraction, if not counter-
acted by some other power, would draw it perpen-
dicularly to the water, at B ; but it is also impelled
by its projectile force, which the attraction of the
denser medium cannot overcome ; the ray, therefore,
acted on by both these powers, moves in a direction
between them, and instead of pursuing its original
course to D, or being implicitly guided by the water
to E, proceeds towards F, so that the ray appears bent
or broken.
Caroline, I understand that very well ; and is not
this the reason that oars appear bent in water?
Ah's. B. It is owing to the refraction of the rays
reflected by the oar ; but this is in passing from a
dense to a rave medium, for you know that the rays,
by means of which you see the oar, pass from water
into air.
Emily. But I do not understand why a refraction
takes place when a ray passes from a dense into a
rare medium ; I should suppose that it would be ra-
ther less, than more, attracted by the latter.
Mrs, B. And it is precisely on that account that
the ray is refracted. C B, fig. 2. represents a ray
passing obliquely from glass into water : glass being
the denser medium, the ray will be more strongly at-
tracted by that which it leaves than by that which it
enters. The attraction of the glass acts in the direc-
tion A B, while the impulse of projection would carry
the ray to F ; it moves, therefore, between these di-
rections towards D.
Emily. So that a contrary refraction takes place
when a ray passes from a dense into a rare mediunk.
a i a
JHT a^lVTd
T •%■
THE REFRACTION OF LIGHT. 22j
Caroline. But does not the attraction of the denser
medium affect the ray before it touches it ?
Mrs. B. The distance at which the attraction of
the denser medium acts upon a ray is so small as to
be insensible ; it appears therefore to be refracted
only at the point at which it passes from one medium
to the other.
Now that you understand the principle of refrac*
tion, I will show you the refraction of a real ray of
light. Do you see the flower painted at the bottom
of the inside of this tea-cup ? (Fig. 3.)
Emily. Yes. — But now you have moved it just
out of sight, the rim of the cup hides it.
Mrs. B. Do not stir. I will fill the cup with wa-
ter, and you will see the flower again.
Emily. I do indeed ! Let me try to explain this :
when you draw the cup from me so «as to conceal the
tiower, the rays reflected by it no longer met my
eyes, but were directed above them ; but now that
you have filled the cup with water, they are refracted
by the attraction of the water, and bent downwards,
so as again to enter my eyes.
Mrs. B. You have explained it perfectly : fig. 3.
will help to imprint it on your memory. You must
observe that when the flower becomes visible by the
refraction of the ray, you do not see it in the situation
which it really occupies, but an image of the flower
higher in the cup ; for as objects always appear to
be situated in the direction of the rays which enter
the eye, the flower will be seen in the direction of
the reflected ray at B.
Emily. Then, when we see the bottom of a clear
stream, of water, the rays which it reflects being re-
fracted in their passage from the water into the air,
will make the bottom appear higher than it really is.
Mrs. B. And the water will consequently appear
more shallow. Accidents have frequently been oc-
casioned by this circumstance ; and boys who are in
the habit of bathing should be cautioned not to trust
to the apparent shallowness of water, as it will always
226 THE REFRACTION OF LIGHT.
prove deeper than it appears ; unless, indeed, they
view it from a boat on the water, which will enable
them to look perpendicularly upon it ; when the rays
from the bottom passing perpendicularly, no refrac-
tion will take place.
The retraction of light prevents our seeing the
heavenly bodies in their real situation : the light they
send to us being refracted in passing into the atmos-
phere, we see the sun and stars in the direction of
the refracted ray ; as described in tig. 4. Plate XIX.,
the dotted line represents the extent of the atmos-
phere, above a portion of the earth, E B E : a ray
of light coming from the sun S, falls obliquely on it at
A, and is refracted to B ; then, since we see the ob-
ject in the direction of the refracted ray, a spectator
at B will see an image of the sun at C, instead of the
real object at S.
Eiuily. But if the sun were immediately over our
heads, its Fays, falling perpendicularly on the atmos-
phere, would not be refracted, and we should then see
the real sun in its true situation.
Mrs. B. You must recollect that the sun is verti-
cal only to the inhabitants of the torrid zone ; its
rays, therefore, are always refracted in these cli-
mates. There is also another obstacle to our seeing
the heavenly bodies in their real situations : light,
though it moves with extreme velocity, is about eight
minutes and a half in its passage from the sun to the
earth : therefore, when the rays reach us, the sun
must have quitted the spot he occupied on their de-
parture ; yet we see him in the direction of those
rays, and consequently in a situation which he had
abandoned eight minutes and a half before.
Emily. When you speak of the sun's motion, you
mean, I suppose, his apparent motion, produced by
the diurnal motion of the earth.
Mrs. B. No doubt; the effect being the same,
whether it is our earth, or the heavenly bodies which
move : it is more easy to represent things as they ap-
pear to be, than as they really are.
THE REFRACTION OF LIGHTS 227
Caroline. During the morning, then, when the
sun is rising towards the meridian, we must rfrom the
length of time the light is in reaching us) see an
image of the sun below that spot which it really oc-
cupies.
Emily. But the refraction of the atmosphere coun-
teracting this effect, we may perhaps, between the
two, see the sun in its real situation.
Caroline. And in the afternoon, when the sun is
sinking in the west, refraction and the length of time
which the light is in reaching the earth, will conspire
to render the image of the sun higher than it really is*
Mrs. B. The refraction of the sun's rays by the
atmosphere prolongs our days, as it occasions our
seeing an image of the sun, both before he rises and
after he sets; for below the horizon, he still shines
upon the atmosphere, and his rays are thence refract-
ed to the earth. So likewise we see an image of the
sun before he rises, the rays that previously fall upon
the atmosphere being reflected to the earth.
Caroline. On the other hand, we must recollect
that light is eight minutes and a half on its journey ; so
that, by the time it reaches the earth, the sun may
perhaps be risen above the horizon.
Emily. Pray do not glass windows refract the
light.
Mrs. B. They do ; but this refraction is not per-
ceptible, because, in passing through a pane of glass
the rays suffer two refractions, which being in contra-
ry directions, produce the same effect as if no refrac-
tion had taken place.
Emily. I do not understand that.
Mrs. B. Fig. b. Plate XIX. will make it clear to
you : A A represents a thick pane of glass seen edge-
ways. When the ray B approaches the glass at C, it
is refracted by it ; and instead of continuing its course
in the same direction, as the dotted line describes, it
passes through the pane to D ; at that point returning
into the air, it is again refracted by the glad's, but in a
contrarv direction t© the first refraction, and in conse-
228 THE REFRACTION OF LIGHT.
quence proceeds to E. Now you must observe that
the ray B C and the ray D E being parallel, the ii^ht
does not appear to have suffered any refraction.
Emily So that the effect which takes place on the
ray entering the glass, is undone on i s quitting it.
Or, to express myself more scientifically, when a ray
of light passes from one medium into another, an^^^
through that into the first again, the two refractiorfs
being equal and in opposite directions, no sensible
effect is produced.
Mrs. B. Thi^ is the case when the two surfaces
of the refracting medium are parallel to each other;
if they are not, the two refractions may be made in the
same direction, as 1 shall show you.
When parallel rays (fig. 6.) fall on a piece of glass
having a double convex surface, and wl)ich is called a
Lens, that only which f tils in the direction of the axis
of the lens is perpentlicular to the surface ; the other
rays falling obliquely are refracted towards the axis,
and will meet at a point beyond the lens, called its
focus.
Of the three rays, A B C, which fdl on the lens D
E, the rays A and C are refracted in their passage
through it, to a, and r, and on quitting the lens they
undergo a second refraction in the same direction,
which unites them with the ray B, at the focus F.
Einilij. And what is the distance of the focus from
the surface of the lens ?
Mrs. B. The focal distance depends both upon the
form of the lens, and of the refractive power of the
substance of which it is made : in a glaes lens, both
sides of wliich are equally convex, the focus is situated
nearly at the centre of the sphere of which the sur-
fiice of the lens forms a portion ; it is at the distance,
therefore, of the radius of the sphere.
There are lenses of various forms, as you will find
described in fig. 1. Plate XX. The property of those
which have a convex surface is to collect the rays of
light to a focus ; and of those which have a concave
surface, on the contrary, to disperse them. For the rays
-%• ^■
PLATE. XT.
m
THE REFRACTION OF LIOHT# ' 2^
A C falling on the concave lens X Y, (fig. 7. Plate
XIX.) instead of converging towards the ray B, wliicK
falls on the axis of the lens, will each be attracted to-
wards the thick edges of the lens, both on entering
and quitting it, and will, therefore, by the first re-
fraction, be made to diverge to a, c, and by the second
to </, e.
Caroline, And lenses which have one side flat and
the other convex or concave, Jis A and B, fig. 1 . Plate
XX., are, I suppose, less powerful in their refrac-
tions ?
Mrs. B. Yes ; they are called plano-convex and
plano-concave lenses : the focus of the former is at
the distance of the diameter of a sphere, of which the
convex surface of the lens forms a portion ; as repre-
sented in fig. 2. Plate XX. The three parallel rays,
ABC, are brought to a focus by the plano-convex
lens X Y at F,
I must now explain to you the refraction of a trian-
gular piece of glass, called a prism. (Fig. 3.)
Emily. The three sides of this glass are flat : it
cannot, therefore, bring the rays to a focus ; nor do
I suppose that its refraction will be similar to that of
a flat pane of glass, because it has not two sides paral-
lel ; I cannot, therefore, conjecture what eflect the
refraction of a prism can produce.
Mrs B. The refractions of the light, on entering
and on quitting the prism, are both in the same direc-
tion. (Fig- 3.) On entering the prism P, the ray
A is refracted from B to C, and on quitting it from C
toD.
1 will show you this in nature ; but for this purpose
it will be advisable to close the window-shutters, and
admit, through the small aperture, a ray of light, which
I shall refract by means of this prism.
Caroline. Oh, what beautiful colours are repre-
sented on the opposite wall ! There are all the co-
lours of the rainbow, and with a brightness 1 never
saw equalled. (Fig. 4. Plate XX.)
Emiiy. i have seen an effect, in some respects si-
20
230 ON REFRACTION AND COLOURS.
milar to this, produced by the rays of the sun shining
upon glass lustres ; but how is it possible that a piece
of white glass can produce such a variety of brilliant
colours ?
Mrs. B. The colours are not formed by the prism,
but existed in the ray previous to its refraction.
Caroline. Yet, before its refraction it appeared
perfectly white.
Mrs. B. The white rays of the sun are composed
of coloured rays, which, when blended together, ap-
pear colourless or white.
Sir Isaac Newton, to whom we are indebted for the
most important discoveries respecting light and co-
lours, was the first who divided a white ray of light,
and found it to consist of an assemblage of coloured
rays, which formed an image upon the wall, such as
you now see exhibited, (fig 4.) in which are display-
ed the following series of colours : red, orange, yel-
low, green, blue, indigo, and violet.
Emily. But how does a prism separate these co-
loured rays ?
Mrs. B. By refraction. It appears that the co-
loured rays have different degrees of refrangibility ;
in passing through the prism, therefore, they take
different directions according to their susceptibility of
refraction. The violet rays deviate most from their
original course ; they appear at one of the ends of
the spectrum A B : contiguous to the violet are the
blue rays, being those which have somewhat less re-
frangibility ; then follow, in succession, the green,
yellow, orange, and, lastly, the red, which are the
least refrangible of the coloured rays.
Caroline. I cannot conceive how these colours,
mixed together, can become white ?
Mrs. B. That I cannot pretend to explain ; but
it is a fact, that the union of these colours, in the pro-
portions in which they appear in the spectrum, pro-
duce in us the idea of whiteness. If you paint a card
in compartments with these seven colours, and whirl
it rapidly on a pin, it will appear white.
ox UEfKACilON AND COLOURS. 231
But a more decisive proof of the composition of a
white ray is afl'orded by re-uniting these coloured rays,
and forming with them a ray of white light.
Caroline. If you can take a ray of white light to
pieces, and put it together again, 1 shall be quite
satisfied.
Mrs. B. This can be done by letting the coloured
rays, which have been separated by a prism, fall
upon a lens, which will converge them to a focus ;
and if, when thus re-united, we lind that they appear
white, as they did before refraction, I hope that you
will be convinced that the white rays are a compound
of the several coloured rays. The prism P, you see,
;fig. 5.) separates a ray of white light into seven co-
loured rays, and the lens L L brings them to a focus
at F, where they again appear white.
Caroline. You succeed to perfection : this is in-
deed a most interesting and conclusive experiment.
Emily. Yet, Mrs. B., I cannot help thinking, that
there may perhaps be but three distinct colours in
the spectrum, red, yellow, and blue ; and that the
four others may consist of two of these colours blend-
ed together ; for, in painting, we find that by mixing
red and yellow, we produce orange ; with different
proportions of red and blue, we make violet or any
shade of purple ; and yellow and blue form green.
Now it is very natural to suppose, that the refraction
of a prism may not be so perfect as to separate the
coloured rays of light completely, and that those
which are contiguous in order of refrangibility may
encroach on each other, and by mixing produce the
intermediate colours, orange, green, violet, and in-
digo.
Mrs. B. Your observation is, I believe, neither
quite wrong, nor quite right. Dr. Wollaston, who
has refracted light in a more accurate manner than
had been previously done, by receiving a very nar-
row line of light on a prism, found that it formed a
spectrum, consisting of rays of four colours only ;
but they were not exactly those you have named as
J3^ ON nEFRACTION AND COLOUR^.
primitive colours, for they consisted of red, green <
blue, and violet. A very narrow line of yellow was
visible at the limit of the red and green, which Dr.
Wollaston attributed to the overlapping of the edges
of the red and green light.
Caroline. But red and green mixed together do
not produce yellow.
Mrs. B. Not in painting : but it may be so in the
primitive rays of the spectrum. Dr. Wollaston ob-
served that, by increasing the breadth of the aperture
by which the line of light was admitted, the space oc-
cupied by each coloured ray in the spectrum was aug-
mented, in proportion as each portion encroached on
the neighbouring colour and mixed with it ; so that
the intervention of orange and yellow, between the
red and green, is owing, he supposes, to the mixture
of these two colours, and the blue is blended on the
ene side with the green, and on the other with the
violet, forming the spectrum as it was originally ob-
served by Sir Isaac Newton, and which 1 have just
shown you.
The rainbow, which exhibits a series of colours so
analogous to those of the spectrum, is formed by the
refraction of the sun's rays in their passage through a
shower of rain, every drop of which acts as a prism,
in separating the coloured rays as they pass through
it.
Emily. Pray, Mrs. B., cannot the sun's rays be
collected to a focus by a lens in the same manner as
they are by a concave mirror ?
Mrs. B. No doubt the same effect is produced by
the refraction of a lens as by the retlection of a con-
cave mirror : in the first, the rays pass through the
glass and converge to a focus behind it ; in the latter,
they are reflected from the mirror, and brought to a
focus before it. A lens, when used for the purpose of
collecting the sun's rays, is called a burning glass.
The sun now shines very bright ; if we let the rays
fall on this lens you will perceive the focus.
Emily. Oh yes : the point of union of the rays is
ON REFRACTION AND COLOURS. 23S
very luminous. I will hold a piece of paper in the
focus, and see if it will take fire. The spot of light is
extremely brilHant, but the paper does not burn ?
Mr». B. Try a piece of brown paper ; — that you
see takes fire almost immediately.
Caroline. This is surprising ; for the light appear-
ed to shine more intensely on the white than on the
brown paper.
Mrs. B. The lens collects an equal number of
Fays to a focus, whether you hold the white or the
brown paper there ; but the white paper appears
more luminous in the focus, because most of the rays,
instead of entering into the paper, are reflected by it :
and this is the reason that the paper is not burnt ;
whilst, on the contrary, the brown paper, which ab-
sorbs more light than it reflects, soon becomes heate4
and takes fire.
Caroline. This is extremely curious ; but why
should brown paper absorb more rays than white pa-
per ?
Mrs. B. I am far from being able to give a satis-
factory answer to that question. We can form but
mere conjecture on this point ; and suppose that
the tendency to absorb, or reflect rays, depends on
the arrangement of the minute particles of the bo-
dy, and that this diversity of arrangement renders
some bodies susceptible of reflecting one coloured
ray, and absorbing the others ; whilst other bodies
have a tendency to reflect all the colours, and others
again, to absorb them all.
Emily. And how do you know which colours bo-
dies have a tendency to reflect : or which to absorb ?
Mrs. B. Because a body always appears to be of
the colour which it reflects ; for, as we see only by
reflected rays, it can appear but of the colour of those
rays.
Caroline. But we see all bodies of their own natu-
ral colour, Mrs. B. ; the grass and trees, green ; the
sky, blue ; the flowers, of various hues.
Mrs. B. True ; but why is the grass green ?-—
20*
234 ox REFRACTION AM) COLOUR;^.
because it absorbs all except the green rays ; it is
therefore these only which the grass and trees reflect
to our eyes, and which makes them appear green.
The sky and flowers, in the same manner, reflect the
various colours of which they appear to us ; the rose,
the red rays ; the violet, the blue ; the jonquil, the
yellow, &c.
Caroline. But these are the permanent colours of
the grass and flowers, whether the sun's rays shine on
them or not.
Mrs. B. Whenever you see those colours, the
flowers must be illumined by some hght ; and light,
from whatever source it proceeds, is of the same na-
ture, composed of the various coloured rays, which
paint the grass, the flowers, and every coloured ob-
ject in nature.
Caroline. But, Mrs. B., the grass is green, and the
flowers are coloured, whether in the dark, or expo-
sed to the light ?
Mrs. B. Why should you think so ?
Caroline. It cannot be otherwise.
Mrs. B. A most philosophical reason indeed 1
But, as I never saw them in the dark, you will allow
me to dissent from your opinion.
Caroline. What colour do you suppose them to be,
then, in the dark ?
Mrs. B. None at all : or black, which is the same
thing. You can never see objects without light.
Light is composed of colours, therefore there can be
no light without colours ; and though every object is
black, or without colour in the dark, it becomes co-
loured as soon as it becomes visible. It is visible,
indeed, but by the coloured rays which it reflects ;
therefore we can see it only when coloured.
Caroline. All you say seems very true, and I know
not what to object to it ; yet it appears at the same
time incredible ! What, Mrs. B., are we all as black
as negroes, in the dark ? you make me shudder at
the thought.
Mrs. B, Your vanity need not be alarmed at the-
ON REFRACTION AND COLOURS. 235
idea, as you are certain of never being seen in that
state.
Caroline. That is some consolation, undoubtedly ;
but what a melancholy reflection it is, that all nature,
which appears so beautifully diversified with colours,
should be one uniform mass of blackness !
Mrs. B. Is nature less pleasing for being colour-
ed, as well as illumined by the rays of light ; and are
colours less beautiful, for being accidental, rather
than essential properties of bodies ?
Providence appears to have decorated nature with
the enchanting diversity of colours, which we so
much admire, for the sole purpose of beautifying the
scene, and rendering it a source of pleasurable enjoy-
ment : it is an ornament which embellishes nature
whenever we behold her. What reason is there to
regret that she does not wear it when she is invisible ?
Emily. 1 confess, Mrs. B., that I have had my
doubts, as well as Caroline, though she has spared
me the pains of expressing them ; but 1 have just
thought of an experiment, which, if it succeeds, will,
1 am sure, satisfy us both. It is certain that we can-
not see bodies in the dark, to know whether they have
then any colour. But we may place a coloured body
in a ray of light, which has been refracted by a
prism ; and if your theory is true, the body, of what-
ever colour it naturally is, must appear of the colour
of the ray in which it is placed ; for since it receives
no other coloured rays, it can reflect no others.
Caroline. Oh ! that is an excellent thought, Emily ;
will you stand the test, Mrs. B. ?
Mrs. B. 1 consent : but we must darken the room,
and admit only the ray which is to be refracted ;
otherwise, the white rays will be reflected on the
body under trial, from various parts of the room.
With what do you choose to make the experiment ?
Caroline. '1 his rose : look at it, Mr.*. B., and tell
me whether it is possible to deprive it of its beautiful
colour ?
Mrs. B. We shall see. — I expose it first to the
236 ©X REFRACTIOX AND COLOURS.
red rays, and the flower appears of a more brilliant
hue ; but observe the green leaves —
Caroline. They appear neither red nor green ;
but of a dingy brown with a reddish glow !
Mrs. B. They cannot be green, because they
have no green rays to reflect ; neither are they red,
because green bodies absorb most of the red rays.
But though bodies, from the arrangement of their
particles, have a tendency to absorb some rays, and
reflect others, yet it is not natural to suppose, that
bodies are so perfectly uniform in their arrangement,
as to reflect only pure rays of one colour, and per-
fectly absorb the others : it is found, on the contrary,
that a body reflects, in great abundance, the rays
which determine its colour, and the others in a greater
or less degree, in proportion as they are nearer or
further from its own colour, in the order of refrangi-
bility. The green leaves of the rose, therefore, will
reflect a few of the red rays, which, blended with
their natural blackness, give them that brown tinge :
if they reflected none of the red rays, they would ap-
pear perfectly black. Now I shall hold the rose in
the blue rays —
Caroline. Oh, Emily, Mrs. B. is right! look at
the rose : it is no longer red, but of a dingy blue co-
lour.
Emily. This is the most wonderful of any thing we
have yet learnt. But, Mrs. B., what is the reason
that the green leaves are of a brighter blue than the
rose ?
Mrs. B. The green leaves reflect both blue and
yellow rays, which produces a green colour. They
are now in a coloured ray, which they have a ten-
dency to reflect ; the}^ therefore, reflect more of
the blue rays than the rose, (which naturally absorbs
that colour,) and will, of course, appear of a brighter
blue.
Emily. Yet, in passing the rose through the differ-
ent colours of the spectrum, the flower takes them
more readily than the leaves.
ON REFRACTION AND COLOURS. 237
.Mrs, B. Because the flower is of a paler hue.
Bodies which reflect all the rays are white ; those
which absorb them all are black : between these ex-
tremes, the body appears lighter or darker, in pro-
portion to the quantity of rays they reflect or absorbs
This rose is of a pale red : it approaches nearer to
white than black ; it therefore reflects rays more
abundantly than it absorbs them.
Emily. But if a rose has so strong a tendency ta
reflect rays, I should have imagined that it would be
of a deep red colour.
Mrs. B. 1 mean to say, that it has a general ten-
dency to reflect rays. Pale-coloured bodies reflect
all the coloured rays to a certain degree, which pro-
duces their paleness, approaching to whiteness : but
one colour they reflect more than the rest ; this
predominates over the white, and determines the
colour of the body. Since, then, bodies of a
pale colour in some degree reflect all the rays of light,
in passing through the various colours of the spec-
trum, they will reflect them all with tolerable brilli-
ancy ; but will appear most vivid in the ray of their
natural colour. The green leaves, on the contrary,
are of a dark colour, bearing a stronger resemblance
to black than to white ; they have, therefore, a
greater tendency to absorb than to reflect rays ; and
reflecting very ie^w of any but the blue and yellow
rays, they will appear dingy in passing through the
other colours of the spectrum.
Caroline. They must, however, reflect great
quantities of the green rays, to produce so deep a co-
lour.
Mrs. B. Deepness or darkness of colour proceeds
rather from a deficiency than an abundance of reflect-
ed rays. Remember that bodies are, of themselves,
black ; and if a body reflects only a few green rays,
it will appear of a dark green, it is the brightness and
intensity of the colour which show that a great quan-
tity of rays are reflected.
Emily. A white body, then, which reflects all the
238 ox IlEFRACTIOX AND COLOURS.
rays, will appear equally bright in all the colours ot
the spectrum.
Mrs. B. Certainly. And this is easily proved by
passing a sheet of white paper through the rays of the
spectrum.
Caroline. What is the reason that blue often ap-
pears green by candle-light?
Mrs. B. The light of a candle is not so pure as
that of the sun : it has a yellowish tinge, and when
refracted by the prism, the yellow rays predominate ;
and as blue bodies reflect the yellow rays in the next
proportion, (being next in order of refrangibility,) the
superabundance of yellow rays gives to blue bodies a
greenish hue.
Caroline. Candle-light must then give to all bodies
a yellowish tinge, from the excess of yellow rays :
and yet it is a common remark, that people of a sal-
low complexion appear fairer or whiter by candle-
light.
Mrs. B. The yellow cast of their complexion is
not so striking when every object has a yellow
linge.
Emily. Pray, why does the sun appear red through
a fog?
Mrs. B. It is supposed to be owing to the red
rays having a greater momentum, which gives them
power to traverse so dense an atmosphere. For the
same reason, the sun generally appears red at rising
and setting : as the increased quantity of atmosphere,
which the oblique rays must traverse, loaded with the
mists and vapours which are usually formed at those
times, prevents the other rays from reaching us.
Caroline. And, pray, why are the skies of a blue
colour?
Mrs. B. You should rather say the atmosphere ;
for the sky is a very vague term, the meaning of
which it would be difficult to define philosophically.
Caroline. But the colour of the atmosphere should
be white, since aJl the rays traverse it in their passage
to the earth.
ON REFRACTION AND COLOURS. 239
Mrs. B. Do not forsjet that we see none of the
rays which pass from the sun to the earth, excepting
those which meet our eyes ; and this happens only if
we look at the sun, and thus intercept the rays, in
which case, you know, the sun appears white. The
atmosphere is a transparent medium, through which
the sun's rays pass freely to the earth ; but when re-
flected back into the atmosphere, their momentum is
considerably diminished ; and they have not all of
them power to traverse it a second time. The mo-
mentum of the blue rays is least ; these, therefore,
are the most impeded in their return, and are chiefly
reflected by the atmosphere : this reflection is per-
formed in every possible direction ; so that whenever
we look at the atmosphere, some of these rays fall
upon our eyes ; hence we see the air of a blue colour.
If the atmosphere did not reflect any rays, though
the objects on the surface of the earth would be illu-
mined, the skies would appear perfectly black.
Caroline. Oh, how melancholy that would be ; and
how pernicious to the sight, to be constantly viewing
bright objects against a black sky. But what is the
reason that bodies often change their colour ; as
leaves which wither in autumn, or a spot of ink which
produces an iron-mould on linen ?
Mrs. B. It arises from some chemical change,
which takes place in the internal arrangement of the
parts, by which they lose their tendency to reflect
certain colours, and acquire the power of reflecting
others. A withered leaf thus no longer reflects the
blue rays ; it appears, therefore, yellow, or has a
slight tendency to reflect several rays which produce
a dingy brown colour.
An ink-spot on linen at first absorbs all the rays ;
but, exposed to the air, it undergoes a chemical
change, and the spot partially regains its tendency to
reflect colours, but with a preference to reflect the
yellow rays, and such is the colour of the iron-mould.
Emily. Bodies, then, far from being of the colour
which they appear to possess, are of that colour which
240 ON REFRACTION AND COLOURb.
they have the greatest aversion to, which they will
not incorporate with, but reject and drive from them.
Mrs. B. It certainly is so ; though 1 scarcely dare
venture to advance such an opinion, whilst Caroline
is contemplating her beautiful rose.
Caroline. My poor rose ! you are not satisfied
with depriving it of colour, but even make it have an
aversion to it ; and 1 am unable to contradict you.
Emily. Since dark bodies absorb more solar rays
than light ones, the former should sooner be heated
if exposed to the sun ?
Mrs. B. And they are found by experience to be
so. Have you never observed a black dress to be
warmer than a white one ?
Emily. Yes, and a white one more dazzling : the
black is heated by absorbing the rays, the white daz-
zling by reflecting them.
Caroline. And ihis was the reason that the brown
paper was burnt in the focus of the lens, whilst the
white paper exhibited the most luminous spot, but
did not take fire.
Mrs. B. It was so. It is now full time to con-
clude our lesson. At our next meeting, 1 shall give
.you a. description of the eye.
TJLATE irXJ.
CONVERSATION XVIf.
OPTICS.
ON THE STRUCTURE OF THE EYE, AND
OPTICAL INSTRUMENTS.
Description of the Eye. — Of the Image on the Retina. —
Refraction of the Humours of the Eye. — Of the Use
of Spectacles. — Of the Single Microscope. — Of the
Double Microscope. — Of the Solar Microscope. —
Magic Lanthorn. — Refracting lelescope. — Reflecting
Telescope.
MRS. B. The body of the eye is of a spherical
form: (fig. 1. Phite XXI.) it has two membranous
coverings ; the external one, « a a, is called the scle-
rotica : this has a projection in that part of the eye
which is exposed to view, h 6, which is called the
cornea, because, when dried, it has nearly the con-
sistence of very fine horn, and is sufficiently transpa-
rent for the light to obtain free passage through it.
The second membrane which lines the cornea, and
envelopes the eye, is called the choroid, c c c; this
has an opening in front, just beneath the cornea,
which forms the pupil, d d, through which the rays
of light pass into the eye. The pupil is surrounded
by a coloured border, called the iris, e e, which, by
its muscular motion, always preserves the pupil of a
circular form, whether it is expanded in the dark, oi-
contracted by a strong light. This you wilLnndor^
stand better by examining fig. 2.
"21
242 OPTICS.
Emily, I did not know that the pupil was suscepu-
ble of varying its dimensions.
Mrs. B. The construction of the eye is so admira-
ble, that it is capable of adapting itself, more or less,
to the circumstances in which it is placed. In a faint
light the pupil dilates so as to receive an additional
quantity of rays, and in a strong light it contracts, in
order to prevent the intensity of the light from injur-
ing the optic nerve. Observe Emily's eyes, as she
gits looking towards the windows : her pupils appear
very small, and the iris large. Now, Emily, turn
from the light, and cover your eyes with your hand,
30 as entirely to exclude it for a few moments.
Caroline. How very much the pupils of her eyes
are now enlarged, and the iris diminished. This is,
no doubt, the reason why the eyes suffer pain, when
from darkness they suddenly come into a strong light ;
for the pupil being dilated, a quantity of rays must
rush in before it has time to contract.
Emily. And when we go from a strong light into
obscurity, we at first imagine ourselves in total dark-
ness; for a sufficient number of rays cannot gain ad-
mittance into the contracted pupil, to enable us to dis-
tinguish objects : but in a few minutes it dilates, and
we clearly perceive objects which were before invi-
sible.
Mrs. B. It is just so. The choroid c c, is imbued
with a black liquor, which serves to absorb all the
rays that are irregularly reflected, and to convert the
body of the eye into a more perfect camera obscura.
When the pupil is expanded to its utmost extent, it
is capable of admitting ten times the quantity of light
that it does when most contracted. In cats, and ani-
mals which are said to see in the dark, the power of
dilatation and contraction of the pupil is still greater:
it is computed that their pupils may receive one hun-
dred times more light at one time than at another.
Within these coverings of the eye-ball are contained
three transparent substances, called humours. The
iirst occupies the space immediately behind the cornea,
OF'ilCSJ.
243
and is called the aqueous humour,//, from its liquidity
and its resemblance to water. Beyond this is situated
the crystalline humour, g g^ so called from its clear-
ness and transparency : it has the form of a lens, and
refracts the rays of light in a greater degree of per-
fection than any that have been constructed by art ;
it is attached by two muscles, m 7n, to each side of
the choroid. The back part of the eye, between the
crystalline humour and the retina, is filled by the vi-
treous humour, h /i, which derives its name from a
resemblance it is supposed to bear to glass or vitrified
substances.
The membranous coverings of the eye are intended
chiefly for the preservation of the retina, i «, which
is by far the most important part of the eye, as it is
that which receives the impression of the objects of
sight, and conveys it to the mind. The retina con-
sists of an expansion of the optic nerve, of a most per-
fect whiteness : it proceeds from the brain, enters
the eye, at n, on the side next the nose, and is finely
spread over the interior surface of the choroid.
The rays of light which enter the eye by the pupil
are refracted by the several humours in their passage
through them, and unite in a focus on the retina.
Caroline. I do not understand the use of these re-
fracting humours : the image of objects is represented
in the camera obscura, without any such assistance.
Mrs. B. That is true ; but the representation
would be much more strong and distinct, if we enlar-
ged the opening of the camera obscura, and received
the rays into it through a lens.
I have told you that rays proceed from bodies in all
possible directions. We must, therefore, consider
every part of an object which sends rays to our eyes,
as points from which the rays diverge, as from a cen-
tre.
Emily. These divergent rays, issuing from a sin-
gle point, I believe you told us, were called a pencil
of rays ?
Mrs. B. Yes. Now, divergent rays, on entering the
244
OPTICS.
pupil, do not cross each other ; the pupil, however.
is sufficiently large to admit a small pencil of them ,
and these, if not refracted to a focus by the humour^?,
would continue diverging after they had passed the
pupil, would fall dispersed upon the retina, and thus
the image of a single point would be expanded over a
large portion of the retina. The divergent rays from
every other point of the object would be spread over
a similar extent of space, and would interfere and be
confounded with the first ; so that no distinct image
could be formed, and the retina would represent to-
tal confusion both of figure and colour. Fig. 3. re-
presents two pencils of rays issuing from two points
of the tree A B, and entering the pupil C, refracted
by the cryst<illine humour D, and forming distinct ima-
ges of the spot they proceed from, on the retina, at a
h. Fig. 4. differs from the preceding, merely from
not being supplied with a lens ; in consequence of
which the pencils of rays are not refracted to a focus,
and no distinct image is formed on the retina. I have
delineated only the rays issuing from two points of aa
object, and distinguished the two pencils in fig. 4. by
describing one of them with dotted lines : the interfe-
rence of these two pencils of rays on the retina will
enable you to form an idea of the confusion which
would arise, from thousands and millions of points at
the same instant pouring their divergent rays upon
the retina.
Emily. True ; but I do not yet well understand
how the refracting humours remedy this imperfec-
tion.
Mrs. B. The refraction of these several humours
unite the whole of a pencil of rays, proceeding from
any one point of an object, to a corresponding point
on the retina, and the image is thus rendered distinct
and strong. If you conceive, in fig. 3., every point
of the tree to send forth a pencil of rays similar to
those, A B, every part of the tree will be as accu-
rately represented on the retina as the points ah.
OPTICS. 245
Emily. How admirably, how wonderfully, this i*
contrived !
Caroline. But since the eye requires refracting
humours in order to have a distinct representation form-
ed on the retina, why is not the same refraction neces-
sary for the image formed in the camera obscura ?
Mrs. B. Because the aperture through which we
received the rays into the camera obscura is
extremely small ; so that but very few of the rays di-
verging from a point gain admittance ; but we will
now enlarge the aperture, and furnish it with a lens,
and you will find the landscape to be more perfectly
represented.
Caroline. How obscure and confused the image is
now that you have enlarged the opening, without put-
ting in the lens.
Mrs. B. Such, or very similar, would be the re-
presentation on the retina, unassisted by the refract-
ing humours. But see what a difference is produced
by the introduction of the lens, which collects each
pencil of divergent rays into their several foci.
Caroline. The alteration is wonderful : the repre-
sentation is more clear, vivid, and beautiful than
ever.
Mrs. B. You will now be able to understand the
nature of that imperfection of sight, which arises from
the eyes being too prominent. In such cases, the
crystalline humour, D, (fig. 6.) being extremely con-
vex, refracts the rays too much, and collects a pencil,
proceeding from the object A B, into a focus, F,
before they reach the retina. From this focus, the
rays proceed diverging, and consequently form a very
confused image on the retina, at a b. This is the de-
fect of short-sighted people.
Emily. I understand it perfectly. But why is this
ilefect remedied by bringing the object nearer to the
eye, as we find to be the case with short-sighted peo-
ple ?
Mrs. B. The nearer you bring an object to your
eye, the more divergent the rays fall upon the crys-
21*
246 OPTICS.
talline humour, and they are consequently not so sooy
converged to a focus : this focus, therefore, either
falls upon the retina, or at least approaches nearer to
it, and the object is proportionally distinct, as in fig. 6.
Emily. The nearer, then, you bring an object to
a lens, the further the image recedes behind it.
Mrs. B. Certainly. But short-sighted persons
have another resource for objects which they cannot
approach to their eyes ; this is to place a concave
lens, C D, (fig. 1. Plate XXII.) before the eye, in
order to increase the divergence of the rays. The
effect of a concave lens is, you know, exactly the re-
verse of a convex one : it renders parallel rays di-
vergent, and those which are already divergent, still
more so. By the assistance of such glasses, there-
fore, the rays from a distant object fall on the pupil,
as divergent as those from a less distant object ; and,
with short-sighted people, they throw the image of a
distant object back as far as the retina.
Caroline. ^ This is an exceUent contrivance,
indeed.
Mrs. B. And tell me, what remedy would you de-
vise for such persons as have a contrary defect in
their sight ; that is to say, in whom the crystalline
humour, being too flat, does not refract the rays sufli-
ciently, so that they reach the retina before they are
converged to a point ?
Caroline. I suppose that a contrary remedy must
be applied to this defect ; that is to say, a convex
lens, L M, fig. 2., to make up for the deficiency of
convexity of the crystalline humour, O P. For the
convex lens would bring the rays nearer together, so
that they would fall either less divergent, or parallel
on the crystalline humour ; and, by being sooner con-
verged to a focus, would fall on the retina.
Mrs. B. V^ery well, Caroline. This is the rear
son why elderly people, the humours of whose eyes
are decayed by age, are under the necessity of using
convex spectacles. And when deprived of that re-
source, they hold the object at a distnace from their
FZATE. jonr.
OPTICS. 24T
eyes, as in fig. 4, in order to bring the focus for-
warder.
Caroline. I have often been surprised, when my
grandffither reads without his spectacles, to see him
hold the book at a considerable distance from his eyes.
But I now understand it ; for the more distant the ob-
ject is from the crystaHine, the nearer the image will
be to it.
Emily. I comprehend the nature of these two op-
posite defects very well ; but 1 cannot now conceive
how any sight can be perfect : for if the crystalline
humour is of a proper degree of convexity, to bring
the image of distant objects to a focus on the retina,
it will not represent near objects distinctly ; and if, on
the contrary, it is adapted to give a clear image of
near objects, it will produce a very imperfect one of
distant objects.
Mrs. B. Your observation is very good, Emily ;
and it is tru-e, that every person would be subject to
one of these two defects, if we had it not in our power
to increase or diminish the convexity of the crystal-
line humour, and to project it towards, or draw it
back from the object, as circumstances require. In
a young well-constructed eye, the two muscles to
which the crystalline humour is attached have so per-
fect a command over it, that the focus of the rays
constantly falls on the retina, and an image is formed
equally distinct both of distant objects and of those
which are near.
Caroline. In the eyes of fishes, which are the only
eyes I have ever seen separate from the head, the
cornea does not protrude, in that part of the eye
which is exposed to view.
Mrs. B. The cornea of the eye of a fish is not
more convex than the rest of the ball of the eye ; but
to supply this deficiency, their crystalline humour is
spherical, and refracts the rays so much, that it does
not require the assistance of the cornea to bring them
to a focus on the retina.
Emily. Pray what is the reason that we cannot seP.
248 OPTICS.
an object distinctly, if we approach it very near to
the eye ?
Mrs. B. Because the rays A»ll on the crystalline
humour too divergent to be refracted to a focus on
the retina ; the confusion, therefore, arising from
viewing an object too near the eye, is similar to that
which proceeds from a flattened crystalline humour ;
the rays reach the retina before they are collected to
a focus, (fig. 4.) If it were not for this imperfection,
we should be able to see and distinguish the parts of
objects, which are now invisible to us from their mi-
nuteness ; for could we approach ihem very near
the eye, their image on the retina would be so much
magnified as to render them visible.
Emily. And could there be no contrivance to con-
vey the rays of objects viewed close to the eye, so
that they should be refracted to a focus on the retina ?
Mrs. B. The microscope is constructed for this
purpose. The single microscope (fig. 5.) consists
simply of a convex lens, commonly called a magnify-
ing glass ; in the focus of which the object is placed,
and through which it is viewed : by this means, you
are enabled to approach your eye very near the ob-
ject, for the lens A B, by diminishing the divergence
of the rays, before they enter the pupil C, makes them
fall parallel on the crystalline humour D, by which
they are refracted to a focus on the retina, at R K.
Emily. This is a most admirable invention, and
nothing can be more simple, for the lens magnifies the
object merely by allowing us to bring it nearer to
the eye.
Mrs. B. Those lenses, therefore, which have the
shortest focus will magnify the object most, because
they enable us to bring the object nearest to the eye.
Emily. But a lens that has the shortest focus is
most bulging or convex ; and the protuberance of the
lens will prevent the eye from approaching very near
to the object.
Mrs. B. This is remedied by making the lens ex-
tremely small : it may then be spherical without oc-
PLATE XXm
OPTICS. 249
cupying much space, and thus unite the advantages of
a short focus, and of allowing the eye to approach the
object.
Caroline. We have a niicroscope at home, which
is a much more complicated instrument than that you
have described.
Mrs. B. It is a double microscope (fig. 6.) in
which you see, not the object A B, but a magnified
image of it, a b. In this microscope two lenses are
employed, the one, L M, for the purpose of magnify-
ing the object, is called the. object glass ; the other,
N O, acts on the principle of the single microscope,
and is called the eye-glass.
There is another kind of microscope, called the
solar microscope, which is the most wonderful from
its great magnifying power : in this we also view an
image formed by a lens, not the object itself. As the
sun shines, I can show you the effect of this micro-
scope ; but for this purpose, we must close the shut-
ters, and admit only a small portion of light, through
the hole in the wiodow-shutter, which we used for
the camera obscura. We shall now place the ob-
ject A B, (Plate XXIII. fig. 1.) which is a small in-
sect, before the lens C D, and nearly at its focas :
the image E F will then be represented on the op-
posite wall in the same manner as the landscape was
in the camera obscura ; with this difference, that it
will be magnified instead of being diminished. I shall
leave you to account for this by examining the figure.
Emily. 1 see it at once. The image E F is mag-
nified, because it is farther from the lens than the
object A B ; while the representation of the land-
scape was diminished, because it was nearer the lens
than the landscape was. A lens, then, answers the
purpose equally well, either for magnifying or dimi-
nishing objects ?
Mrs. B. Yes : if you wish to magnify the image,
you place the object near the focus of the lens ; if you
wish to produce a diminished image, you place the
250 OPTICS.
object at a distance from the lens, in order that the
image may be formed in, or near the focus.
Carolne. The magnifying power of this micro-
scope, is prodigious ; but the indistinctness of the
image, for want of light, is a great imperfection.
Would it not be clearer if the opening in the shutter
were enlarged so as to admit more light.
Mrs. B. If the whole of the light admitted does
not fall upon the object, the effect will only be to
make the room lighter, and the image consequently
less distinct.
Emily. But could you not by means of another
lens bring a large pencil of rays to a focus on the ob-
ject, and thus concentrate tkt whole of the light ad-
mitted upon it ?
Mrs. B. Very well. We shall enlarge the open-
ing, and place the lens X Y (fig. 2.) in it, to converge
the rays to a focus on the object A B. There is but
one thing more wanting to complete the solar micro-
scope, which I shall leave to Caroline's sagacity to
discover.
Caroline. Our microscope has a small mirror at-
tached to it, upon a moveable joint, which can be so
adjusted as to receive the sun's rays, and reflect them
upon the object : if a similar mirror were placed to
reflect light upon the lens, would it not be a means
of illuminating the object more perfectly.
Mrs. B. You are quite right. P Q (fig. 2.) is a
small mirror, placed on the outside of the window-
shutter, which receives the incident rays S S, and
reflects them on the lens X Y. Now that we have
completed the apparatus, let us examine the mites on
this piece of cheese, which I place near the focus of
the lens.
Caroline. Oh, how much more distinct the image
now is, and how wonderfully magnified ! The mites
on the cheese look like a drove of pigs scrambling
over rocks.
Emily. I never saw any thing so curious. Now,
an immense piece of cheese has fallen : one would
OPTICS. 251
imagine it an earthquake : some of the poor mites
must have been crushed ; how fast they run, — they
absolutely seem to gallop.
But this microscope can be used only for transpa-
rent objects ; as the light must pass through them to
form the image on the wall ?
Mrs. B. Very minute objects, such as are view-
ed in a microscope, are generally transparent ; but
when opaque objects are to be exhibited, a mirror
M N (tig 3.) is used to reflect the light on the side of
the object next the wall : the image is then formed
by light reflected from the object, instead of being
transmitted through it.
Emily. Pray, is not a magic lanthorn constructed
on the same principles 1
Mrs. B. Yes ; with this difierence, that the light
is supplied by a lamp instead of the sun.
The microscope is an excellent invention, to ena-
ble us to see and distinguish objects which are too
small to be visible to the naked eye. But there are
objects which, though not really small, appear so to
us, from their distance ; to these we cannot apply the
same remedy ; for when a house is so far distant as to
be seen under the same Hngle as a mite which is close
to us, the eff*ect produced on the retina is the same :
the angle it subtends is not large enough for it to
form a distinct image on the retina.
Emily. Since it is impossible, in this case, to ap-
proach the object to the eye, cannot we by means of
a lens bring an image of it nearer to us ?
Mrs. B. Yes ; but then, the object being very
distant from the focus of the lens, the image would
be too small to be visible to tfie naked eye.
Emily. Then why not look at the image through
another lens, which will act as a microscope, enable
us to bring the image close to the eye, and thus ren-
der it visible ?
Mrs. B. Very well, Emily ; I congratulate you on
having invented a telescope. In figure 4, the lens
C D, forms an image E F, of the object A B ; and the
252, OPTICS.
lens X Y serves the purpose of magnifying that
image ; and this is all that is required in a common re-
fracting telescope.
Emily. But in fig. 4, the image is not inverted on
the retina, as objects usually are : it should therefore
appear to us inverted ; and that is not the case in the
telescopes I have looked through.
Mrs. B. When it is necessary to represent the
image erect, two other lenses are required ; by which
means a second image is formed, the reverse of the
first, and consequently upright. These additional
glasses are used to view terrestrial objects ; for no
inconvenience arises from seeing the celestial bodies
inverted.
Emily. The difference bctwppn a microscope and
a telescope, seems to be this ; — a microscope produ-
ces a magnified image, because the object is nearest
the lens ; and a telescope produces a diminished im-
age, because the object is furthest from the lens.
Mrs. B. Your observation applies only to the lens
C D, or object-glass, which serves to bring an image
of the object nearer the eye ^ for the lens X Y, or
eye-glass, is, in fact, a microscope, as its purpose is
t(D magnify the image.
When a very great magnifying power is required,
telescopes are constructed with concave mirrors, in-
stead of lenses. Concave mirrors, you know, pro-
duce, by redection, an effect similar to that of convex
lenses by refraction. In reflecting telescopes, there-
fore, mirrors are used in order to bring the image
nearer the eye ; and a lens or eye-glass the same
as in the refracting telescope to magnify the image.
The advantage of the reflecting telescope is, that
mirrors whose focus is six feet will magnify as much
;is lenses of a hundred feet.
Caroline. But I thought it was the eye-glass only
which magnified the image ; and that the other lens
served to bring a diminished image nearer to the eye.
Mrs. B. The image is diminished in comparison to
the object, it is true ; but it is magnified if you com-
OPTICS. 2J^J
pare it to the dimensions of* which it would appear
without the intervention of any optical instrument ;
and this magnifying power is greater in reflecting than
in refracting telescopes.
We must now hring our observations to a conclu-
sion, for I have communicated to you tlie whole of my
very limited stock of knowledge of Natural Philoso-
phy. If it will enable you to make further progress
in that science, my wishes will be sati«tied ; biit re-
member that, in order that the study of nature may be
productive of happiness, it must lead to an entire con-
fidence in the wisdom and goodness of its bounteous
Author.
2JJ
INDEX.
Air, 16. 21. 35. 63. 168. 202.
225.
Air-pump, 40. 170.
Angle, 56.
, acute, 67.
, obtuse, 57.
of incidence, 57. 199.
215.
of reflection, 58. 190.
199. 215.
of vision, 209. 210.
Aphelion, 96.
Arctic circle, 115. 125.
Atmosphere, 129. 160. 168. 180.
202.
, reflection of, 184.
, colour of, 238.
, refraction of, 223.
227.
Attraction, 15.20.30.223.
, of cohesion, 20 43.
147. 168.
-, of gravitation, 25.
Barometer, 173.
Bass, 192.
Bladder, 170.
Bodies, 14.
, elastic, 51. 62.
, luminous, 194.
, sonorous, 186.
, fall of, 30. 34. 39. 47.
, opaque, 194. 223.
, transparent, 194, 223
Bulk, 22.
Camera obscura, 203. 214. 249.
Capillary tubes, 24.
Centre, 61.
■ of gravity, 61. 65. 68.
70. 142.
of motion, 61. 69. 142.
of magnitude, 61. 67.
41.90. 102 120. 141. 168.
Avenue, 209. 210.
Auditory Nerve, 191.
Axis, 99.
of motion, 61. 70.
of the earth, 115. 123.
of mirrors, 217.
of a lens, 228.
B
Balloon, 39.
Centrifugal force, 63. 93. 118.
142.
Centripetal force, 63. 93.
Ceres, 106.
Circle, 66 117. 119.
Circular motion, 60. 93.
Clouds, 159
Colours, 30. 229.
Comets, 107.
Compression, 53.
Concord. 192.
Constellation, 108.
Convergent rays, 217. 219.
Crystals, 17.
Cylinder, 66.
256
INDEX.
D
Day, 99. 180.
Degrees, 56. 117 123.212.
of latitude, 118 138.
of longitude, 1 18. 138.
Density, 22.
Diagonal. 60.
Diameter, 117.
Diurnal, 99.
Discords, 191.
Divergent rays, 217.
Divisibility, 15. 17.
E
£artli,25.90. 106. 112. 114
Echo, 189.
Eclipse, 135. 139. 197.
Ecliptic, 109. 116.
Elastic bodies, 51. 53.
fluids, 21. 37. 147. 168.
Ellipsis, 95.
Essential properties, 15.
Exhalations, 18.
Extension, 15. 16.
Equator, 115.
Equinox, 124. 126.
-, precession of, 132.
Eye, 203.
Fal! of bodies, 30. 34. 39. 47.
Figure, 15 17.
Fluids, 146.
, elastic, 147. 168.
' , equilibrium of, 148. 173.
, pressure of, 149. 163. 1 72.
Flying, 51.
Focus, 218.
of convex mirrors, 218.
of concave;220.
. of a lens, 228.
Force, 42.
centrifugal, 63. 93. lis.
Force of gravity, 25. 90. 102.
169.
Fountains: 167.
Friction, 87. 167.
Frigid zone, 117. 124.
Fulcrum, 70.
General properties of bodies,
14. 15.
Georgium Sidus, 107.
Glass, 227.
, refraction of, 227.
burning, 232.
Gold, 154.
Gravity, 25. 30—41. 43. 47. 64
65.
H
Harmony, 192.
Heat, 22. 129.
Hemisphere, 115. 124.
Hydrometer, 157.
Hydrostatics, 146.
Image on the retina, 204. 213
Image reversed, 206.
in plain mirror, 214.
in convex ditto, 217.
in concave, 217.
142.
, centripetal, 63.93.
of projection. 63 92.
Impenetrability, 15.
Inclined plane, 69.84,
Inertia, 15. 20. 42.
Juno, 106
Jupiter, 106. 139.
Lake, 165.
Latitude, US. 138.
Lens, 228.
, convex, 228.
, concave, 22S
LWIXEX.
357
Lever, (59.
, first order, 74.
, second ditto, 76.
. third ditto, 77.
Light. 195.
, jieDcil of, 195.
, rpflrcted, 198.
of the moon, 200.
, refraction of, 220.
, absorption of, 233.
Liquid, 147.
Longitude, 118 138.
Luminous bodies, 194.
Lunar month, 1.34.
eclipse, 135.
M
Machine, 69. 84. 87.
Mat{ic lanthorn, 251.
Mars, 106.
Matter, 14. 49.
Mecrhanics, 69.
Mediums, 195. 223.
Melody, 193.
Mercury planet, 105 140.
Mercury, or quicksilver, 178.
Meridians, 117.
Microscope, 248 252.
, single, 248.
, double, 249.
. , solar, 249.
Minerals, 17.
Minutes, 117.
Monsoons, 183.
Month, lunar, 134.
Momentum, 49. 73
Moon,101.102. 107. 134. 141.
Moon-light. 200.
Motion, 20. 42. 49. 50.
uniform, 44.
, perpetual, 45.
, retarded , 46.
, accelerated, 46.
, reflected, 55.
, compound, 59.
, circular, 60. 94.
, axis of, 61 . 70.
, centre of, 61. 69, 142.
, diurnal, 99.
Musical instruments, 192.
Mirrors, 214.
, reflection of, 214.
, plain Of flat, 217.
, convex, 217.
, concave. 217. 219
, axis of, 217.
, burning, 221.
N
Neap tides, 143.
Nerves, 204.
, auditory, 191 20&.
, optic, 203. 205,
, olfactory, 205.
Night, 99.
Nodes, 123. 124, 132,
Octave, 192.
Odour, 18.
Opaque bodies, 194. 196.
Optics. 194.
Orbit, 104.
Pallas, 106.
Parabola, 64.
Parallel lines, 33.
Pellucid bodies, 195,
Pencil of ray?, 196.
Pendulum, 121.
Perihelion, 96.
Perpendicular lines, 33. 56. 127-.
Phases, 135.
Piston, 176.
Plane, 116.
Planets, 97. 102. 130.
Poles, 115
Polar star, 124. 138.
Pond, 165.
Porosity, 54.
Power, mechanical, 69.
Projection, 63. 92.
Precession of the equinoxe?,
132.
Pulley, 69. 79.
258
INDEX.
Pump, 40. 4i.
, sucking, or lifting, 176.
, forcing, 178. 180.
Pupil of the eye, 203.
R
Rain, 160.
Rainbow, 232.
Rarity, 22.
Ray of light, 195.
of reflection, 199.
of incidence, 199.
Rays, intersecting, 203.
Reaction, 60.
Receiver, 40.
Reflection of light, 198.
, angle of, 68. 215.
of mirrors, 214.
of plain mirrors, 217.
of convex mirrors,
217.
i — of concave mirrors,
217.
Reflected motion, 55.
Refraction, 220.
of the atmosphere,
227.
of glass, 227.
of a lens, 228.
of a prism, 229.
Resistance, 69.
Retina, 203.
, image on, 204.
Rivers, 159.
Rivulets, 162.
S
Satellites, 102. 137. 139.
Saturn, 106.
Scales or balance, 70.
Screw, 69. 85.
Shadow, 136. 196.
Sidereal time, 132.
Sight, 204.
Signs, Zodiac, 108. 116. 118.
Smoke, 19. 38.
Solar microscope, 249.
Solstice, 123. 125.
Sound, 185.
, acute, 191.
, musical, 192.
Space, 43.
Specific gravity, 152.
of air, 173
Spectrum, 230.
Speaking trumpet, 190.
Sphere, 33. 66. 120.
Springs, 161.
Spring tides, 143.
Square, 60. 103. 107.
Stars. 97. 108. 131.138.
Storms, 181
Substance, 14,
Summer, 96. 123.
Sun, 90. 102 194.226.
Swimming, 52.
Syphon, 164.
Tangent, 63 93.
Telescope, 251.
. — , reflecting, 252
, refracting. 252.
Temperate zone^ 117. 126.
Thermometer, 175.
Tides, 141.
, neap, 143.
, spring, 143.
, aerial. 185.
Time, 130. 133.
, sidereal. 132.
, equal, 133.
, solar, 133.
Tone, 191.
Torrid zone, 116. 125. 181.
Transparent bodies, 194.
Treble and bass, 192.
Tropics, 115.
Valve, 177.
Vapour, 23. 38. 16(^
Velocity, 43. 72.
Venus, 105, 140.
Vesta, 106
Vibration. ISP.
INDEX.
259
Vihion, 20d.
, angle of, 209.
, double, 213.
U
Undulations, 188.
Unison, 192.
W
Waters, 147.
, spring, 161.
, rain, 161.
, level of, 148. 154 159.
VVed^e, 69 85
Weit?ht, 22. 30. 120. 152. 169.
170.
Wheel aad a&le, 69. 83.
Wind, 180.
, trade, 182.
, periodical, 183.
Winch, 86.
Winter, 96. 125.
Year, 180.
, sidf-real, 132
, solar, 133.
Zodiac, 108. 118.
Zone, 116.
, torrid, 116. 125. 181 . 226
, temperate, 117. 125.
, frigid, 117. 124.
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